Search

Potentials in cosmological inflation often involve scalars with trans-Planckian ranges. As a result, towers of states become massless and their presence pushes the fundamental scale not to coincide with $M_{\rm P}$ but rather with the $species\, scale$, $\Lambda$. This scale transforms as an automorphic form of the theory's duality symmetries. We propose that the inflaton potential should be 1) an automorphic invariant form, non-singular over all moduli space, 2) depending only on $\Lambda$ and its field derivatives, and 3) approaching constant values in the large moduli to ensure a long period of inflation. These conditions lead to the proposal $V \sim \lambda(\phi, \phi^*)$, with $\lambda = G^{i\bar{j}} (\partial_i \Lambda)(\partial_{\bar{j}} \Lambda) / \Lambda^2$, determining the 'species scale convex hull'. For a single elliptic complex modulus with $SL(2, Z)$ symmetry, this results in an inflaton potential $V \simeq (\text{Im} \tau)^2 |\tilde{G}_2|^2 / N^2$, with $N \simeq -\log(\text{Im} \tau |\eta(\tau)|^4)$, where $\eta$ is the Dedekind function and $\tilde{G}_2$ the Eisenstein modular form of weight 2. Surprisingly, this potential at large modulus resembles that of the Starobinsky model. We compute inflation parameters yielding results similar to Starobinsky's, but extended to modular invariant expressions. Interestingly, the number of e-folds is proportional to the number of species in the tower, $N_e \simeq N$, and $\epsilon \simeq \Lambda^4$ at large moduli, suggesting that the tower of states plays an important role in the inflation process., Comment: 21 pages + appendices, 3 figures. v2: references added, minor changes

We study how tiny Dirac neutrino masses consistent with experimental constraints can arise in string theory SM-like vacua. We use as a laboratory 4d ${\cal N}=1$ type IIA Calabi--Yau orientifold compactifications, and in particular recent results on Yukawa couplings at infinite field-space distance. In this regime we find Dirac neutrino masses of the form $m_\nu \simeq g_\nu\langle H\rangle$, with $g_{\nu}$ the gauge coupling of the massive $U(1)$ under which the right-handed neutrinos $\nu_R$ are charged, and which should be in the range $g_{\nu}\simeq 10^{-14}-10^{-12}$ to reproduce neutrino data. The neutrino mass suppression occurs because the right-handed neutrino kinetic term behaves as $K_{\nu\nu} \simeq 1 /g_{\nu}^2 $. At the same time a tower of $\nu_R$-like states appears with characteristic scale $m_0\simeq g_{\nu}^2M_{\rm P}\simeq 0.1-500$ eV, in agreement with Swampland expectations. Two large hidden dimensions only felt by the $\nu_R$ sector arise at the same scale, while the string scale is around $M_s\simeq g_\nu M_{\rm P}\simeq 10-700$ TeV. Some phenomenological implications and model building challenges are described. As a byproduct, independently of the neutrino issue, we argue that a single large dimension in the context of SM-like type IIA Calabi--Yau orientifolds leads to too small Yukawa couplings for quarks and charged leptons., Comment: 31 pages + appendices, 4 figures, 4 tables. v2: references added; Appendix updated

We study limits of vanishing Yukawa couplings of 4d chiral matter fields in Quantum Gravity, using as a laboratory type IIA orientifolds with D6-branes. In these theories chiral fermions arise at brane intersections, where an infinite tower of charged particles dubbed gonions are localised. We show that in the limit $Y\rightarrow 0$ some of these towers become asymptotically massless, while at the same time the kinetic term of some chiral fields becomes singular and at least two extra dimensions decompactify. For limits parametrised by a large complex structure saxion $u$, Yukawa couplings have a behaviour of the form $Y \, \sim \, {1}/{u^r}$, with $r$ some positive rational number. Moreover, in this limit some of the gauge couplings associated to the Yukawa vanish. The lightest gonion scales are of order $m_{\rm gon} \sim g^s M_{\rm P}$ with $s>1$, verifying the magnetic WGC with room to spare and with no need of its tower/sublattice versions. We also show how this behaviour can be understood in the context of the emergence of kinetic terms in Quantum Gravity. All these results may be very relevant for phenomenology, given the fact that some of the Yukawa couplings in the Standard Model are very small., Comment: 56 pages + appendices, 9 figures, 7 tables. v4: JHEP version

The concept of the species scale as the quantum gravity cut-off has been recently emphasised in the context of the Swampland program. Along these lines, we continue the quest for a precise understanding of its role within effective field theories of gravity as well as a global definition of the latter in case there is enough supersymmetry preserved. To do so, we exploit duality symmetries, the familiar asymptotic dependence imposed by the presence of infinite towers of light states and the known behaviour of higher-curvature corrections to the Einstein-Hilbert action in various String Theory setups. In those cases, we obtain a self-consistent result for the identification of the species scale as the quantum gravity cut-off, but also present some puzzles related to the suppression of certain higher-dimensional operators as well as minor ambiguities that may arise in the deep interior of moduli space., Comment: Minor changes, references added and Section 4 significantly extended. Matches the published version

The Swampland Distance Conjecture (SDC) states that, as we move towards an infinite distance point in moduli space, a tower of states becomes exponentially light with the geodesic distance in any consistent theory of Quantum Gravity. Although this fact has been tested in large sets of examples, it is fair to say that a bottom-up justification that explains both the geodesic requirement and the exponential behavior has been missing so far. In the present paper we address this issue by making use of the Covariant Entropy Bound as applied to the EFT. When applied to backgrounds of the Dynamical Cobordism type in theories with a moduli space, we are able to recover these main features of the SDC. Moreover, this naturally leads to universal lower and upper bounds on the 'decay rate' parameter $\lambda_{\text{sp}}$ of the species scale, that we propose as a convex hull condition under the name of Species Scale Distance Conjecture (SSDC). This is in contrast to already proposed universal bounds, that apply to the SDC parameter of the lightest tower. We also extend the analysis to the case in which asymptotically exponential potentials are present, finding a nice interplay with the asymptotic de Sitter conjecture. To test the SSDC, we study the convex hull that encodes the (asymptotic) moduli dependence of the species scale. In this way, we show that the SSDC is the strongest bound on the species scale exponential rate which is preserved under dimensional reduction and we verify it in M-theory toroidal compactifications., Comment: v2: minor changes and typos corrected. 54 pages + Appendix, 17 figures, 2 tables

Based on Quantum Gravity arguments, it has been suggested that all kinetic terms of light particles below the UV cut-off could arise in the IR via quantum (loop) corrections. These loop corrections involve infinite towers of states becoming light (e.g. Kaluza-Klein or string towers). We study implications of this Emergence Proposal for fundamental scales in the Standard Model (SM). In this scheme all Yukawa couplings are of order one in the UV and small Yukawas for lighter generations appear via large anomalous dimensions induced by the towers of states. Thus, the observed hierarchies of quark and lepton masses are a reflection of the structure of towers of states that lie below the Quantum Gravity scale, $\Lambda_{\text{QG}}$. Small Dirac neutrino masses consistent with experimental observation appear due to the existence of a tower of SM singlet states of mass $m_{0}\simeq Y_{\nu_3}M_p\simeq 7\times 10^5$ GeV, opening up a new extra dimension, while the UV cut-off occurs at $\Lambda_{\text{QG}}\lesssim 10^{14}$ GeV. Additional constraints relating the Electro-Weak (EW) and cosmological constant (c.c.) scales (denoted $M_{\text{EW}}$ and $V_0$) appear if the Swampland condition $m_{\nu_1}\lesssim V_0^{1/4}$ is imposed (with $\nu_1$ denoting the lightest neutrino), which itself arises upon applying the AdS non-SUSY Conjecture or the AdS/dS Distance Conjecture to the 3d vacua from circle compactifications of the SM. In particular, the EW scale and that of the extra dimension fulfill ${m_0 \, M_{\text{EW}}\lesssim 10^{2}\, V_0^{1/4}M_p}$, thus relating the EW hierarchy problem to that of the c.c. Hence, all fundamental scales may be written as powers of the c.c., i.e. $m_{\bullet}\sim V_0^\delta M_p^{1-4\delta}$. The scale of SUSY breaking is $m_{3/2}\lesssim 7\times 10^5$ GeV, which favours a Mini-Split scenario that could be possibly tested at LHC and/or FCC., Comment: 20 pages, 5 figures, 1 table; v2: references added and typos corrected

In the Emergence Proposal in QG it is conjectured that all light-particle kinetic terms are absent in the fundamental UV theory and are generated by quantum corrections in the IR. It has been argued that this may provide for some microscopic understanding of the WGC and SDC. In the present paper we take the first steps towards a systematic study of Emergence in the context of string theory. We emphasize the crucial role of the species scale in any EFT coupled to gravity, and discuss its computation in string theory and general systems with light towers of states. We then introduce the notion of Emergence and show how kinetic terms for moduli, gauge bosons and fermions may be generated. One-loop computations play an important role in Emergence, so we present detailed calculations in $d$ spacetime dimensions for the wave-function renormalization of scalars, vectors and fermions. We extend and check the Emergence Proposal in a number string vacua, including 4d $\mathcal{N}=2$ theories arising from type IIA on a CY$_3$, where the towers at strong coupling are comprised by D0 and (wrapped) D2-branes, and also elaborate on how instanton corrections would fit within the emergence picture. Higher dimensional examples are also discussed, including 6d and 7d models arising from F-/M-theory on an elliptic CY$_3$ or a $K3$ surface. We also consider 10d string theories and study in some detail the emergence mechanism in type IIA. We show as well how the flux potential in 4d may be obtained from the emergence prescription, by analyzing the corresponding decompactification limits to M-theory. We find that the required kinetic terms for the dual 3-form fields can arise upon integrating out towers of massive gravitini (and bosonic superpartners). Our analysis renders support to the Emergence Proposal, and to the idea that infinite distance singularities may arise in QG as an intrinsic IR phenomenon., Comment: v2: minor changes and typos corrected. 79 pages + Appendices, 11 figures, 8 tables

By applying the Covariant Entropy Bound (CEB) to an EFT in a box of size $1/\Lambda_{\text{IR}}$ one obtains that the UV and IR cut-offs of the EFT are necessarily correlated. We argue that in a theory of Quantum Gravity (QG) one should identify the UV cutoff with the `species scale', and give a general algorithm to calculate it in the case of multiple towers becoming light. One then obtains an upper bound on the characteristic mass scale of the tower in terms of the IR cut-off, given by $M_{\text{tower}}\lesssim (\Lambda_{\text{IR}})^{2\alpha_D}$ in Planck units, with $\alpha_D=(D-2+p)/2p(D-1)$, where $p$ depends on the density of states. Identifying the IR cut-off with a (non-vanishing) curvature in AdS one reproduces the statement of the AdS Distance Conjecture (ADC), also giving an explicit lower bound for the $\alpha$ exponent. In particular, we find that the CEB implies $\alpha \geq1/2$ in any dimension if there is a single KK tower, both in AdS and dS vacua. However values $\alpha <1/2$ are allowed if the particle tower is multiple or has a string component. We also consider the CKN constraint coming from avoiding gravitational collapse which further requires in general $\alpha \geq 1/D$ for the lightest tower. We analyse the case of the DGKT-CFI class of Type IIA orientifold models and show it has both particle and string towers below the species scale, so that a careful analysis of how the ADC is defined is needed. We find that this class of models obey but do not saturate the CEB. The UV/IR constraints found apply to both AdS and dS vacua. We comment on possible applications of these ideas to the dS Swampland conjecture as well as to the observed dS phase of the universe., Comment: 19 pages, 4 figures. v2: minor corrections, references added. v3: minor corrections and comments added

We conjecture that in a consistent supergravity theory with non-vanishing gravitino mass, the limit $m_{3/2}\rightarrow 0$ is at infinite distance. In particular one can write $M_{\mathrm{tower}} \sim m_{3/2}^\delta$ so that as the gravitino mass goes to zero, a tower of KK states as well as emergent strings becomes tensionless. This conjecture may be motivated from the Weak Gravity Conjecture as applied to strings and membranes and implies in turn the AdS Distance Conjecture. We test this proposal in classical 4d type IIA orientifold vacua in which one obtains a range of values $\tfrac13 \le \delta \le 1$. The parameter $\delta$ is related to the scale decoupling exponent in AdS vacua and to the $\alpha$ exponent in the Swampland Distance Conjecture for the type IIA complex structure. We present a general analysis of the gravitino mass in the limits of moduli space in terms of limiting Mixed Hodge Structures and study in some detail the case of two-moduli F-theory settings. Moreover, we obtain general lower bounds $\delta\, \geq \, \frac{1}{3}, \, \frac{1}{4}$ for Calabi--Yau threefolds and fourfolds, respectively. The conjecture has important phenomenological implications. In particular we argue that low-energy supersymmetry of order 1 TeV is only obtained if there is a tower of KK states at an intermediate scale, of order $10^8$ GeV. One also has an upper bound for the Hubble constant upon inflation $H \lesssim m_{3/2}^\delta M^{(1-\delta)}_{\text{P}}$., Comment: v2: 60 pages, 3 figures. Minor changes and references added

We consider constraints on $D$-dimensional theories in $M_D$, $dS_D$ and $AdS_D$ backgrounds in the light of AdS swampland conjectures as applied to their compactification in a circle. In particular we consider the non-SUSY AdS instability conjecture and the AdS distance conjecture. For $M_D$ and $dS_D$ vacua the results may be summarized by a light fermion conjecture which states that in theories with $\Lambda_D\geq 0$ and a positive first non-vanishing supertrace $(-1)^{k+1}\text{Str} M^{2k}>0$, a surplus of light fermions with mass $m_f\lesssim \Lambda_D^{1/D}$ must be present. On the contrary, the cases of $M_D$ and $AdS_D$ can be made consistent with the mild but not the strong version of the AdS Distance conjecture, since the KK tower in the lower $d$-dim theory will scale as $m\lesssim \Lambda_d^{\alpha}$ with $\alpha=1/d$. The above constraints also suggest that the Standard Model of particle physics would be inconsistent in Minkowski space but consistent in dS if the lightest neutrino is Dirac and lighter than the cosmological constant scale., Comment: Minor corrections. References added

The Weak Gravity Conjecture (WGC) is usually formulated in terms of the stability of extremal black-holes or in terms of long distance Coulomb/Newton potentials. However one can think of other physical processes to compare the relative strength of gravity versus other forces. We argue for an alternative formulation in terms of particle pair production at threshold or, equivalently, pair annihilation at rest. Imposing that the production rate by any force mediator (photon or scalar) of pairs of charged particles be larger or equal to graviton production, we recover known conditions for the $U(1)$ WGC and its extensions. Unlike other formulations though, threshold pair production is sensitive to short range couplings present in scalar interactions and gives rise to a Scalar WGC. Application to moduli scalars gives rise to specific conditions on the trilinear and quartic couplings which involve first and second derivatives of the WGC particle mass with respect to the moduli. Some extremal solutions to these equations correspond to massive states behaving like BPS, KK and winding states which feature duality invariance and are in agreement with the Swampland distance conjecture. Conditions for $N=2$ BPS states saturate our bounds and we discuss specific examples of BPS states which become massless at large Kahler moduli in Type IIA N=2, D=4 CY and orbifold compactifications. We study possible implications for potentials depending on moduli only through WGC massive states. For some simple classes of potentials one recovers constraints somewhat similar but not equivalent to a Swampland dS conjecture., Comment: Diagrammatic derivation of the Strong Scalar PPWGC included in section 5. Minor corrections

We study the separation of AdS and Kaluza-Klein (KK) scales in type II 4d AdS orientifold vacua. We first address this problem in toroidal/orbifold type IIA vacua with metric fluxes, corresponding to compactifications in twisted tori, both from the 4d and 10d points of view. We show how the naive application of the effective 4d theory leads to results which violate the AdS distance conjecture, in a class of $\mathcal{N}=1$ supersymmetric models which have a 10d lifting to a compactification on $S^3\times S^3$. We show how using KK scales properly modified by the compact metric leads to no separation of scales with $M^2_{\text{KK}} = \mathfrak{c} |\Lambda|$, with $\mathfrak{c}$ a numerical constant independent of fluxes. This applies with no need to keep non-leading fluxes fixed. We also consider a class of IIB models with non-geometric fluxes in which the effective field theory analysisseems to lead to a naive separation of scales and a violation of the AdS distance conjecture. It has a T-dual which again may be understood as a 10d type IIA theory compactified on $S^3\times S^3$. In this geometric dual one again observes that the strong AdS distance conjecture is obeyed with $M^2_{\text{KK}} = \mathfrak{c}' |\Lambda|$, if one takes into account the curvature in the internal space. These findings seem to suggest that all toroidal/orbifold models with fluxes in this class obey $M^2_{\text{KK}} = \mathfrak{c} |\Lambda|$ with $\mathfrak{c}$ a flux-independent numerical constant., Comment: 16 pages. References added and minor changes in notation. Published version

The Swampland Distance Conjecture states that at infinite distance in the scalar moduli space an infinite tower of particles become exponentially massless. We study this issue in the context of 4d type IIA and type IIB Calabi-Yau compactifications. We find that for large moduli not only towers of particles but also domain walls and strings become tensionless. We study in detail the case of type IIA and IIB ${\cal N}=1$ CY orientifolds and show how for infinite K\"ahler and/or complex structure moduli towers of domain walls and strings become tensionless, depending on the particular direction in moduli space. For the type IIA case we construct the monodromy orbits of domain walls in detail. We study the structure of mass scales in these limits and find that these towers may occur at the same scale as the fundamental string scale or the KK scale making sometimes difficult an effective field theory description. The structure of IIA and IIB towers are consistent with mirror symmetry, as long as towers of exotic domain walls associated to non-geometric fluxes also appear. We briefly discuss the issue of emergence within this context and the possible implications for 4d vacua., Comment: 69 pages, 5 figures, 8 tables

We propose a new version of the scalar Weak Gravity Conjecture (WGC) which would apply to any scalar field coupled to quantum gravity. For a single scalar it is given by the differential constraint $V''\leq (2V'''^2/V''-V'''')M_{\text{p}}^2$. It corresponds to the statement that self-interactions of a scalar must be stronger than gravity for any value of the scalar field. We find that the solutions which saturate the bound correspond to towers of extremal states with mass $m^2(\phi)=m_0^2/((R/m)^2+1/(nR)^2)$, with $R^2=e^\phi$, consistent with the emergence of an extra dimension at large or small $R$ and the existence of extended objects (strings). These states act as WGC states for the scalar $\phi$. It is also consistent with the distance swampland conjecture with a built-in duality symmetry. From this constraint one can derive several swampland conjectures. In particular one finds that an axion potential is only consistent if $f\leq M_{\text{p}}$. The conjecture has far reaching consequences and applies to several interesting physical systems: i) Among chaotic inflation potentials only those asymptotically linear may survive. ii) If applied to the radion of the circle compactification of the Standard Model to 3D, the constraint implies that the 4D cosmological constant scale must be larger than the mass of the lightest neutrino, which must be Dirac and in normal hierarchy. iii) It also constraints simplest moduli fixing string models. The simplest KKLT model is compatible with the constraints but the latter may be relevant for some choices of parameters., Comment: More accurate version of condition (1.5) given. Higgs-like example discussed. Section on inflation improved. References added

Recent string theory tests of swampland ideas like the distance or the dS conjectures have been performed at weak coupling. Testing these ideas beyond the weak coupling regime remains challenging. We propose to exploit the modular symmetries of the moduli effective action to check swampland constraints beyond perturbation theory. As an example we study the case of heterotic 4d $\mathcal{N}=1$ compactifications, whose non-perturbative effective action is known to be invariant under modular symmetries acting on the K\"ahler and complex structure moduli, in particular $SL(2,Z)$ T-dualities (or subgroups thereof) for 4d heterotic or orbifold compactifications. Remarkably, in models with non-perturbative superpotentials, the corresponding duality invariant potentials diverge at points at infinite distance in moduli space. The divergence relates to towers of states becoming light, in agreement with the distance conjecture. We discuss specific examples of this behavior based on gaugino condensation in heterotic orbifolds. We show that these examples are dual to compactifications of type I' or Horava-Witten theory, in which the $SL(2,Z)$ acts on the complex structure of an underlying 2-torus, and the tower of light states correspond to D0-branes or M-theory KK modes. The non-perturbative examples explored point to potentials not leading to weak coupling at infinite distance, but rather diverging in the asymptotic corners of moduli space, dynamically forbidding the access to points with global symmetries. We perform a study of general modular invariant potentials and find that there are dS maxima and saddle points but no dS minima, and that all examples explored obey the refined dS conjecture., Comment: Minor Corrections. 41 pages, 4 figures

Compactifying the SM down to 3D or 2D one may obtain AdS vacua depending on the neutrino mass spectrum. It has been recently shown that, by insisting in the absence of these vacua, as suggested by {\it Weak Gravity Conjecture} (WGC) arguments, intriguing constraints on the value of the lightest neutrino mass and the 4D cosmological constant are obtained. For fixed Yukawa coupling one also obtains an upper bound on the EW scale $\left\langle H\right\rangle\lesssim {\Lambda_4^{1/4}} /{Y_{\nu_{i}}}$,where $\Lambda_4$ is the 4D cosmological constant and $Y_{\nu_{i}}$ the Yukawa coupling of the lightest (Dirac) neutrino. This bound may lead to a reassessment of the gauge hierarchy problem. In this letter, following the same line of arguments, we point out that the SM without a Higgs field would give rise to new AdS lower dimensional vacua. Absence of latter would require the very existence of the SM Higgs. Furthermore one can derive a lower bound on the Higgs vev $\left\langle H\right\rangle\gtrsim \Lambda_{\text{QCD}}$ which is required by the absence of AdS vacua in lower dimensions. The lowest number of quark/lepton generations in which this need for a Higgs applies is three, giving a justification for family replication. We also reassess the connection between the EW scale, neutrino masses and the c.c. in this approach. The EW fine-tuning is here related to the proximity between the c.c. scale $\Lambda_4^{1/4}$ and the lightest neutrino mass $m_{\nu_i}$ by the expression $ \frac {\Delta H}{H} \lesssim \frac {(a\Lambda_4^ {1/4} -m_{\nu_i})} {m_{\nu_i}}. $ We emphasize that all the above results rely on the assumption of the stability of the AdS SM vacua found., Comment: 11 pages, 3 figures

We present a conjecture for the massless sector of perturbative 4D $N=1$ heterotic $(0,2)$ string vacua, including $U(1)^n$ gauge symmetries,one of them possibly anomalous (like in standard heterotic compactifications). Mathematically it states that the positive hull generated by the charges of the massless chiral multiplets spans a sublattice of the full charge lattice. We have tested this conjecture in many heterotic $N=1$ compactifications in 4D. Our motivation for this conjecture is that it allows to understand a very old puzzle in $(0,2)$ $N=1$ heterotic compactification with an anomalous $U(1)$. The conjecture guarantees that there is always a D-flat direction cancelling the FI-term and restoring $N=1$ SUSY in a nearby vacuum. This is something that has being verified in the past in a large number of cases, but whose origin has remained obscure for decades. We argue that the existence of this lattice of massless states guarantees the instability of heterotic non-BPS extremal blackholes, as required by Weak Gravity Conjecture arguments. Thus the pervasive existence of these nearby FI-cancelling vacua would be connected with WGC arguments., Comment: 11 pages, no figures

It has been recently argued that an embedding of the SM into a consistent theory of quantum gravity may imply important constraints on the mass of the lightest neutrino and the cosmological constant $\Lambda_{4}$. The constraints come from imposing the absence of any non-SUSY AdS stable vacua obtained from any consistent compactification of the SM to 3 or 2 dimensions. This condition comes as a corollary of a recent extension of the Weak Gravity Conjecture (WGC) by Ooguri and Vafa. In this paper we study $T^2/Z_N$ compactifications of the SM to two dimensions in which SM Wilson lines are projected out, leading to a considerable simplification. We analyze in detail a $T^ 2/Z_4$ compactification of the SM in which both complex structure and Wilson line scalars are fixed and the potential is only a function of the area of the torus $a^2$. We find that the SM is not robust against the appearance of AdS vacua in 2D and hence would be by itself inconsistent with quantum gravity. On the contrary, if the SM is embedded at some scale $M_{SS}$ into a SUSY version like the MSSM, the AdS vacua present in the non-SUSY case disappear or become unstable. This means that WGC arguments favor a SUSY version of the SM, independently of the usual hierarchy problem arguments. In a $T^2/Z_4$ compactification in which the orbifold action is embedded into the $B-L$ symmetry the bounds on neutrino masses and the cosmological constant are recovered. This suggests that the MSSM should be extended with a $U(1)_{B-L}$ gauge group. In other families of vacua the spectrum of SUSY particles is further constrained in order to avoid the appearance of new AdS vacua or instabilities. We discuss a possible understanding of the little hierarchy problem in this context., Comment: Minor corrections, references added, 2 figures added. 58 pages, 15 figures, 3 tables

We compute the full classical 4d scalar potential of type IIA Calabi-Yau orientifolds in the presence of fluxes and D6-branes. We show that it can be written as a bilinear form $V = Z^{AB} \rho_A\rho_B$, where the $\rho_A$ are in one-to-one correspondence with the 4-form fluxes of the 4d effective theory. The $\rho_A$ only depend on the internal fluxes, the axions and the topological data of the compactification, and are fully determined by the Freed-Witten anomalies of branes that appear as 4d string defects. The quadratic form $Z^{AB}$ only depends on the saxionic partners of these axions. In general, the $\rho_A$ can be seen as the basic invariants under the discrete shift symmetries of the 4d effective theory, and therefore the building blocks of any flux-dependent quantity. All these polynomials may be obtained by derivation from one of them, associated to a universal 4-form. The standard N=1 supergravity flux superpotential is uniquely determined from this {\it master polynomial}, and vice versa., Comment: 75 pages, one figure; v2 minor corrections

It has been recently argued that Higgsing of theories with $U(1)^n$ gauge interactions consistent with the Weak Gravity Conjecture (WGC) may lead to effective field theories parametrically violating WGC constraints. The minimal examples typically involve Higgs scalars with a large charge with respect to a $U(1)$ (e.g. charges $(Z,1)$ in $U(1)^2$ with $Z\gg 1$). This type of Higgs multiplets play also a key role in clockwork $U(1)$ theories. We study these issues in the context of heterotic string theory and find that, while indeed there is no new physics at the standard magnetic WGC scale $\Lambda\sim g_{IR} M_P$, the string scale is just slightly above, at a scale $\sim \sqrt{k_{IR}}\Lambda$. Here $k_{IR}$ is the level of the IR $U(1)$ worldsheet current. We show that, unlike the standard magnetic cutoff, this bound is insensitive to subsequent Higgsing. One may argue that this constraint gives rise to no bound at the effective field theory level since $k_0$ is model dependent and in general unknown. However there is an additional constraint to be taken into account, which is that the Higgsing scalars with large charge $Z$ should be part of the string massless spectrum, which becomes an upper bound $k_{IR}\leq k_0^2$, where $k_0$ is the level of the UV currents. Thus, for fixed $k_0$, $Z$ cannot be made parametrically large. The upper bound on the charges $Z$ leads to limitations on the size and structure of hierarchies in an iterated $U(1)$ clockwork mechanism., Comment: 12 pages

In this addendum we complement the remarks made in ref[1] constraining the value of the cosmological constant $\Lambda_4$ in terms of neutrino masses. Those were based on a sharpened version of the Weak Gravity Conjecture as applied to compactifications of the SM to lower dimensions. We argue that the same line of reasoning implies that for fixed values of $\Lambda_4$ and the Yukawa coupling of the lightest neutrino $Y_{\nu_1}$, the EW scale is bounded above. This is a trivial consequence of neutrino masses depending on the Higgs vev. In the case of massive Majorana neutrinos with a see-saw mechanism associated to a large scale $M\simeq 10^{10-14}$ GeV and $Y_{\nu_1}\simeq 10^{-3}$, one obtains that the EW scale cannot exceed $M_{EW}\lesssim 10^2-10^4$ GeV. From this point of view, the delicate fine-tuning required to get a small EW scale would be a mirage, since parameters yielding higher EW scales would be in the swampland and would not count as possible consistent theories. This would bring a new perspective into the issue of the EW hierarchy., Comment: 3 pages, 2 figures

It is known that there are AdS vacua obtained from compactifying the SM to 2 or 3 dimensions. The existence of such vacua depends on the value of neutrino masses through the Casimir effect. Using the Weak Gravity Conjecture, it has been recently argued by Ooguri and Vafa that such vacua are incompatible with the SM embedding into a consistent theory of quantum gravity. We study the limits obtained for both the cosmological constant $\Lambda_4$ and neutrino masses from the absence of such dangerous 3D and 2D SM AdS vacua. One interesting implication is that $\Lambda_4$ is bounded to be larger than a scale of order $m_\nu^4$, as observed experimentally. Interestingly, this is the first argument implying a non-vanishing $\Lambda_4$ only on the basis of particle physics, with no cosmological input. Conversely, the observed $\Lambda_4$ implies strong constraints on neutrino masses in the SM and also for some BSM extensions including extra Weyl or Dirac spinors, gravitinos and axions. The upper bounds obtained for neutrino masses imply (for fixed neutrino Yukawa and $\Lambda_4$) the existence of upper bounds on the EW scale. In the case of massive Majorana neutrinos with a see-saw mechanism associated to a large scale $M\simeq 10^{10-14}$ GeV and $Y_{\nu_1}\simeq 10^{-3}$, one obtains that the EW scale cannot exceed $M_{EW}\lesssim 10^2-10^4$ GeV. From this point of view, the delicate fine-tuning required to get a small EW scale would be a mirage, since parameters yielding higher EW scales would be in the swampland and would not count as possible consistent theories. This would bring a new perspective into the issue of the EW hierarchy., Comment: 41 pages, 21 figures, 5 tables. v2: Added section 6 + fig.12 + references; typos corrected

We study closed-string moduli stabilization in Higgs-otic inflation in Type IIB orientifold backgrounds with fluxes. In this setup large-field inflation is driven by the vacuum energy of mobile D7-branes. Imaginary selfdual (ISD) three-form fluxes in the background source a $\mu$-term and the necessary monodromy for large field excursions while imaginary anti-selfdual (IASD) three-form fluxes are sourced by non-perturbative contributions to the superpotential necessary for moduli stabilization. We analyze K\"ahler moduli stabilization and backreaction on the inflaton potential in detail. Confirming results in the recent literature, we find that integrating out heavy K\"ahler moduli leads to a controlled flattening of the inflaton potential. We quantify the flux tuning necessary for stability even during large-field inflation. Moreover, we study the backreaction of supersymmetrically stabilized complex structure moduli and the axio-dilaton in the K\"ahler metric of the inflaton. Contrary to previous findings, this backreaction can be pushed far out in field space if a similar flux tuning as in the K\"ahler sector is possible. This allows for a trans-Planckian field range large enough to support inflation., Comment: 42 pages, 10 figures, v2: comments and references added. Published version

We construct models in which the SM Higgs mass scans in a landscape. This is achieved by coupling the SM to a monodromy axion field through Minkowski 3-forms. The Higgs mass scans with steps given by delta(m_H^2)= eta mu f, where mu and f are the axion mass and periodicity respectively, and eta measures the coupling of the Higgs to the associated 3-form. The observed Higgs mass scale could then be selected on anthropic grounds. The monodromy axion may have a mass mu in a very wide range depending on the value of eta, and the axion periodity f. For eta=1 and f = 10^10 GeV, one has 10^{-3}eV < mu < 10^3 eV, but ultralight axions with e.g. mu = 10^{-17} eV are also possible. In a different realization we consider landscape models coupled to the MSSM. In the context of SUSY, 4-forms appear as being part of the auxiliary fields of SUSY multiplets. The scanning in the 4-forms thus translate into a landscape of vevs for the N=1 auxiliary fields and hence as a landscape for the soft terms. This could provide a rationale for the MSSM fine-tuning suggested by LHC data. In all these models there are 3-forms coupling to membranes which induce transitions between different vacua through bubble nucleation. The Weak Gravity Conjecture (WGC) set limits on the tension of these membranes and implies new physics thresholds well below the Planck scale. More generaly, we argue that in the case of string SUSY vacua in which the Goldstino multiplet contains a monodromy axion the WGC suggests a lower bound on the SUSY breaking scale m_{3/2} > M_s^2/M_p., Comment: 28 pages, 1 pdf figure

In string theory compactifications it is common to find an effective Lagrangian for the scalar fields with a non-canonical kinetic term. We study the effective action of the scalar position moduli of Type II D$p$-branes. In many instances the kinetic terms are in fact modified by a term proportional to the scalar potential itself. This can be linked to the appearance of higher-dimensional supersymmetric operators correcting the K\"ahler potential. We identify the supersymmetric dimension-eight operators describing the $\alpha'$ corrections captured by the D-brane Dirac-Born-Infeld action. Our analysis then allows an embedding of the D-brane moduli effective action into an $\mathcal N = 1$ supergravity formulation. The effects of the potential-dependent kinetic terms may be very important if one of the scalars is the inflaton, since they lead to a flattening of the scalar potential. We analyze this flattening effect in detail and compute its impact on the CMB observables for single-field inflation with monomial potentials., Comment: 25 pages, 3 figures. Comments and references added. Published version

Low scale string models naturally have axion-like pseudoscalars which couple directly to gluons and photons (but not $W$s) at tree level. We show how they typically get tree level masses in the presence of closed string fluxes, consistent with the axion discrete gauge symmetry, in a way akin of the axion monodromy of string inflation and relaxion models. We discuss the possibility that the hints for a resonance at 750 GeV recently reported at ATLAS and CMS could correspond to such a heavy axion state (megaxion). Adjusting the production rate and branching ratios suggests the string scale to be of order $M_s$ ~ $7 - 10^4$ TeV, depending on the compactification geometry. If this interpretation was correct, one extra $Z'$ gauge boson could be produced before reaching the string threshold at LHC and future colliders., Comment: 26 pages, 3 figures, 1 Megaxion

The recently proposed relaxion models require extremely large trans-Planckian axion excursions as well as a potential explicitly violating the axion shift symmetry. The latter property is however inconsistent with the axion periodicity, which corresponds to a gauged discrete shift symmetry. A way to make things consistent is to use monodromy, i.e. both the axion and the potential parameters transform under the discrete shift symmetry. The structure is better described in terms of a 3-form field $C_{\mu \nu \rho}$ coupling to the SM Higgs through its field strength $F_4$. The 4-form also couples linearly to the relaxion, in the Kaloper-Sorbo fashion. The extremely small relaxion-Higgs coupling arises in a see-saw fashion as $g\simeq F_4/f$, with $f$ being the axion decay constant. We discuss constraints on this type of constructions from membrane nucleation and the Weak Gravity Conjecture. The latter requires the existence of membranes, whose too fast nucleation could in principle drive the theory out of control, unless the cut-off scale is lowered. This allows to constrain relaxion models on purely theoretical grounds. We also discuss possible avenues to embed this structure into string theory., Comment: 26 pages + appendices, 3 figures; v3: Corrected bounds on relaxion parameter space

We discuss the role of Minkowski 3-forms in flux string vacua. In these vacua all internal closed string fluxes are in one to one correspondence with quantized Minkowski 4-forms. By performing a dimensional reduction of the $D=10$ Type II supergravity actions we find that the 4-forms act as auxiliary fields of the Kahler and complex structure moduli in the effective action. We show that all the RR and NS axion dependence of the flux scalar potential appears through the said 4-forms. Gauge invariance of these forms then severely restricts the structure of the axion scalar potentials. Combined with duality symmetries it suggests that all perturbative corrections to the leading axion scalar potential $V_0$ should appear as an expansion in powers of $V_0$ itself. These facts could have an important effect e.g. on the inflaton models based on F-term axion monodromy. We also suggest that the involved multi-branched structure of string vacua provides for a new way to maintain interacting scalar masses stable against perturbative corrections., Comment: 39 pages. Typos corrected and added references

We propose that inflation is driven by a (complex) neutral Higgs of the MSSM extension of the SM, in a chaotic-like inflation setting. The SUSY breaking soft term masses are of order $10^{12}-10^{13}$ GeV, which is identified with the inflaton mass scale and is just enough to stabilise the SM Higgs potential. The fine-tuned SM Higgs has then a mass around 126 GeV, in agreement with LHC results. We point out that the required large field excursions of chaotic inflation may be realised in string theory with the (complex) inflaton/Higgs identified with a continuous Wilson line or D-brane position. We show specific examples and study in detail a IIB orientifold with D7-branes at singularities, with SM gauge group and MSSM Higgs sector. In this case the inflaton/Higgs fields correspond to D7-brane positions along a two-torus transverse to them. Masses and monodromy are induced by closed string $G_3$ fluxes, and the inflaton potential can be computed directly from the DBI+CS action. We show how this action sums over Planck suppressed corrections, which amount to a field dependent rescaling of the inflaton fields, leading to a linear potential in the large field regime. We study the evolution of the two components of the Higgs/inflaton and compute the slow-roll parameters for purely adiabatic perturbations. For large regions of initial conditions slow roll inflation occurs and 50-60 efolds are obtained with r>0.07, testable in forthcoming experiments. Our scheme is economical in the sense that both EWSB and inflation originate in the same sector of the theory, all inflaton couplings are known and reheating occurs efficiently., Comment: 71 pages, 18 colour figures; typos corrected and added references

It has been recently pointed out that the polarization BICEP2 results are consistent with the identification of an inflaton mass m \simeq 10^{13} GeV with the SUSY breaking scale in an MSSM with a fine-tuned SM Higgs. This identification leads to a Higgs mass m_h \simeq 126 GeV, consistent with LHC measurements. Here we propose that this naturally suggests to identify the inflaton with the heavy MSSM Higgs system. The fact that the extrapolated Higgs coupling lambda_{SM}\simeq 0 at scales below the Planck scale suggests the Higgs degrees of freedom could be associated to a Wilson line or D-brane position modulus in string theory. The Higgs system then has a shift symmetry and an N=2 structure which guarantees that its potential has an approximate quadratic chaotic inflation form. These moduli in string compactifications, being compact, allow for a trans-Planckian inflaton field range analogous to a version of monodromy inflation., Comment: 6 pages. Misprints corrected, references added

Closed string fluxes induce generically SUSY-breaking soft terms on supersymmetric type IIB orientifold compactifications with D3/D7 branes. This was studied in the past by inserting those fluxes on the DBI+CS actions for adjoint D3/D7 fields, where D7-branes had no magnetic fluxes. In the present work we generalise those computations to the phenomenologically more relevant case of chiral bi-fundamental fields laying at 7-brane intersections and F-theory local matter curves. We also include the effect of 7-brane magnetic flux as well as more general closed string backgrounds, including the effect of distant (anti-)D3-branes. We discuss several applications of our results. We find that squark/slepton masses become in general flux-dependent in F-theory GUT's. Hypercharge-dependent non-universal scalar masses with a characteristic sfermion hierarchy m_E^2 < m_L^2 < m_Q^2 < m_D^2 < m_U^2 are obtained. There are also flavor-violating soft terms both for matter fields living at intersecting 7-branes or on D3-branes at singularities. They point at a very heavy sfermion spectrum to avoid FCNC constraints. We also discuss the possible microscopic description of the fine-tuning of the EW Higgs boson in compactifications with a MSSM spectrum., Comment: 67 pages, 2 figures, 2 tables

Recent BICEP2 results on CMB polarisation B-modes suggest a high value for the inflation scale $V_0^{1/4} \simeq 10^{16}$ GeV, giving experimental evidence for a physical scale in between the EW scale and the Planck mass. We propose that this new high scale could be interpreted as evidence for a high SUSY breaking scale $M_{ss}\simeq 10^{12}-10^{13}$ GeV. We show that such a large value for $M_{ss}$ is consistent with a Higgs mass around 126 GeV. We briefly discuss some possible particle physics implications of this assumption., Comment: 5 pages, 1 figure. v2: references added

We argue that in large classes of string compactifications with a MSSM-like structure substantial flavor violating SUSY-breaking soft terms are generically induced. We specify to the case of flavor dependent soft-terms in type IIB/F-theory SU(5) unified models, although our results can be easily extended to other settings. The Standard Model (SM) degrees of freedom reside in a local system of 7-branes wrapping a 4-fold S in the extra dimensions. It is known that in the presence of closed string 3-form fluxes SUSY-breaking terms are typically generated. We explore the generation dependence of these soft terms and find that non-universalities arise whenever the flux varies over the 4-fold S. These non-universalities are parametrically suppressed by (M_{GUT}/M_{Pl})^{1/3}. They also arise in the case of varying open string fluxes, in this case parametrically suppressed by \alpha_{GUT}^{1/2}. For a standard unification scheme with M_{GUT} = 10^{16} GeV and \alpha_{\rm GUT} = 1/24 these suppressions are very mild. Although limits from the kaon mass difference \Delta m_K are easily obeyed for squark masses above the present LHC limits, constraints from the CP-violation parameter \epsilon_K imply squark masses in the multi-TeV region. The constraints from BR(\mu \rightarrow e\gamma) turn out to be the strongest ones, with slepton masses of order ~10 TeV or heavier required to obey the experimental limits. These sfermion masses are consistent with the observed large value m_H ~ 126 GeV of the Higgs mass. We discuss under what conditions such strong limits may be relaxed allowing for SUSY particle production at LHC., Comment: 38 pages, 6 figures, 1 table; v2: references added

We compute the mass of the Higgs particle in a scheme in which SUSY is broken at a large scale M_{SS} well above the electroweak scale M_{EW}. Below M_{SS} one assumes one is just left with the SM with a fine-tuned Higgs potential. Under standard unification assumptions one can compute the mass of the Higgs particle as a function of the SUSY breaking scale M_{SS}. For M_{SS} > 10^{10} GeV one obtains m_H=126 \pm 3 GeV, consistent with CMS and ATLAS results. For lower values of M_{SS} the values of the Higgs mass tend to those of a fine-tuned MSSM with m_H < 130 GeV. These results support the idea that the measured value of the Higgs mass at LHC may be considered as indirect evidence for the existence of SUSY at some (not necessarily low) mass scale., Comment: 25 pages, 7 figures. Slight changes in figures. Conclusions unchanged

Local SU(5) F-theory models lead naturally to Yukawa couplings for the third generation of quarks and leptons, but inducing Yukawas for the lighter generations has proven elusive. Corrections coming from gauge fluxes fail to generate the required couplings, and naively the same applies to instanton effects. We nevertheless revisit the effect of instantons in F-theory GUT constructions and find that contributions previously ignored in the literature induce the leading non-perturbative corrections to the Yukawa couplings. We apply our results to the case of 10 x 5* x 5* couplings in local SU(5) F-theory GUTs, showing that non-perturbative effects naturally lead to hierarchical Yukawas. The hypercharge flux required to break SU(5) down to the SM does not affect the holomorphic Yukawas but does modify the profile of the wavefunctions, explaining the difference between the D-quark and lepton couplings at the unification scale. The combination of non-perturbative corrections and magnetic fluxes allows to describe the measured lepton and D-quark masses of second and third generations in the SM., Comment: minor corrections and references added

Even if SUSY is not present at the Electro-Weak scale, string theory suggests its presence at some scale M_{SS} below the string scale M_s to guarantee the absence of tachyons. We explore the possible value of M_{SS} consistent with gauge coupling unification and known sources of SUSY breaking in string theory. Within F-theory SU(5) unification these two requirements fix M_{SS} ~ 5 x 10^{10} GeV at an intermediate scale and a unification scale M_c ~ 3 x 10^{14} GeV. As a direct consequence one also predicts the vanishing of the quartic Higgs SM self-coupling at M_{SS} ~10^{11} GeV. This is tantalizingly consistent with recent LHC hints of a Higgs mass in the region 124-126 GeV. With such a low unification scale M_c ~ 3 x 10^{14} GeV one may worry about too fast proton decay via dimension 6 operators. However in the F-theory GUT context SU(5) is broken to the SM via hypercharge flux. We show that this hypercharge flux deforms the SM fermion wave functions leading to a suppression, avoiding in this way the strong experimental proton decay constraints. In these constructions there is generically an axion with a scale of size f_a ~ M_c/(4\pi)^2 ~ 10^{12} GeV which could solve the strong CP problem and provide for the observed dark matter. The prize to pay for these attractive features is to assume that the hierarchy problem is solved due to anthropic selection in a string landscape., Comment: 48 pages, 8 figures. v3: further minor corrections

These notes are based on lectures given at the Les Houches Summer School in 2011, which was centered on the general topic "Theoretical Physics to face the challenge of LHC". In these lectures I reviewed a number of topics in the field of String Phenomenology, focusing on orientifold/F-theory models yielding semi-realistic low-energy physics. The emphasis was on the extraction of the low-energy effective action and the possible test of specific models at LHC. These notes are a brief summary, appropriately updated, of some of the main topics covered in the lectures., Comment: 28 pages, 9 figures

In particle physics model building discrete symmetries are often invoked to forbid unwanted or dangerous couplings. A classical example is the R-parity of the MSSM, which guarantees the absence of dimension four baryon- and lepton-number violating operators. Although phenomenologically useful, these discrete symmetries are, in the context of field theory, poorly motivated at a more fundamental level. Moreover, discrete {\em global} symmetries are expected to be violated in consistent couplings to quantum gravity, while their {\em gauged} versions are expected to actually exist. In this paper we study discrete gauge symmetries in brane models in string theory, and argue that they are fairly generic in this framework. In particular we study the appearance of discrete gauge symmetries in (MS)SM brane constructions in string theory, and show that a few discrete ${Z_N}$ gauge symmetries, including R-parity and {\it baryon triality}, appear naturally as remnants of continuous U(1) gauge symmetries with St\"uckelberg $N(B\wedge F)$ couplings. Interestingly, they correspond to the simplest anomaly-free discrete symmetries of the MSSM as classified in the early 90's. We provide a number of examples based on type IIA intersecting brane constructions with a (MS)SM spectrum. We also study the appearance of discrete generalizations of R-parity in unified SU(5) type IIA orientifolds and local F-theory SU(5) GUTs., Comment: 46 pages, v2, minor changes, references added

Type II string compactifications to 4d generically contain massless Ramond-Ramond U(1) gauge symmetries. However there is no massless matter charged under these U(1)'s, which makes a priori difficult to measure any physical consequences of their existence. There is however a window of opportunity if these RR U(1)'s mix with the hypercharge $U(1)_Y$ (hence with the photon). In this paper we study in detail different avenues by which $U(1)_{RR}$ bosons may mix with D-brane U(1)'s. We concentrate on Type IIA orientifolds and their M-theory lift, and provide geometric criteria for the existence of such mixing, which may occur either via standard kinetic mixing or via the mass terms induced by St\"uckelberg couplings. The latter case is particularly interesting, and appears whenever D-branes wrap torsional $p$-cycles in the compactification manifold. We also show that in the presence of torsional cycles discrete gauge symmetries and Aharanov-Bohm strings and particles appear in the 4d effective action, and that type IIA St\"uckelberg couplings can be understood in terms of torsional (co)homology in M-theory. We provide examples of Type IIA Calabi-Yau orientifolds in which the required torsional cycles exist and kinetic mixing induced by mass mixing is present. We discuss some phenomenological consequences of our findings. In particular, we find that mass mixing may induce corrections relevant for hypercharge gauge coupling unification in F-theory SU(5) GUT's., Comment: 68 pages, 2 figures, 7 tables; v2: minor typos corrected, references modified

We study the deformation induced by fluxes and instanton effects on Yukawa couplings involving 7-brane intersections in local F-theory constructions. In the absence of non-perturbative effects, holomorphic Yukawa couplings do not depend on open string fluxes. On the other hand instanton effects (or gaugino condensation on distant 7-branes) do induce corrections to the Yukawas. The leading order effect may also be captured by the presence of closed string (1,2) IASD fluxes, which give rise to a non-commutative structure. We check that even in the presence of these non-perturbative effects the holomorphic Yukawas remain independent of magnetic fluxes. Although fermion mass hierarchies may be obtained from these non-perturbative effects, they would give identical Yukawa couplings for D-quark and Lepton masses in SU(5) F-theory GUT's, in contradiction with experiment. We point out that this problem may be solved by appropriately normalizing the wavefunctions. We show in a simple toy model how the presence of hypercharge flux may then be responsible for the difference between D-quarks and Lepton masses in local SU(5) GUT's., Comment: 84 pages, 1 figure. v2: minor corrections and references added

Recent developemnts in string compactifications in the presence of antisymmetric field backgrounds suggest a new simple and predictive structure for soft terms in the MSSM depending only on two parameters. They give rise to a positive definite scalar potential, a solution to the $\mu $-problem, flavor universality and absence of a SUSY-CP problem., Comment: 23 pages, no figures. Addendum on intersecting D7-branes included. Referencese added and minor changes

We use compact D=4, N=1, Type IIB orientifolds as a testing ground for recent ideas about precocious gauge coupling unification and a low energy string scale. We find that certain such orientifolds have the interesting property that gauge couplings receive moduli-dependent corrections which mimic the effect of field theoretical logarithmic running. The effective cut-off scale for the logarithmic correction is not $M_{string}$ but rather $M_X=\sqrt{\alpha}M_{Planck}M_c/M_{string}$, where $M_c$ is the compactification scale. Thus there is just normal logarithmic running up to $M_{string}$ and extra moduli dependent corrections which behave as if there was further running to a higher virtual scale $M_X$. In this mechanism a prominent role is played by anomalous U(1)'s with moduli dependent Fayet-Iliopoulos terms. A vanishing FI-term fixes the modulus dependence of the corrected gauge coupling. We discuss possible ways to implement this mechanism in the context of a simple extension of the MSSM., Comment: 15 pages, 1 figure; Important clarification which affects conclussions

After a review of some topics concerning the phenomenological applications of perturbative string theory, I discuss to what extent all of it is affected by the recent developements in string dualities., Comment: 35 pages, LaTex . Minor corrections. References added. To appear in the proceedings of the Workshop on Phenomenological Applications of String Theory (PAST), ICTP, Trieste (Italy), October 1997

Supersymmetric N=1, D=4 string vacua are known to be finite in perturbation theory. However, the effective low energy D=4, N=1 field theory lagrangian does not yield in general finite theories. In this note we present the first (to our knowledge) such an example. It may be constructed in three dual ways: i) as a $Z_3$, SO(32) heterotic orbifold; ii) as a Type -IIB, $Z_3$ orientifold with only ninebranes and a Wilson line or iii) as a Type-IIB, $Z_6$ orientifold with only fivebranes. The gauge group is $SU(4)^3$ with three chiral generations. Although chiral, a subsector of the model is continuosly connected to a model with global N=4 supersymmetry. From the $Z_6$, Type IIB orientifold point of view the above connection may be understood as a transition of four dynamical fivebranes from a fixed point to the bulk. The N=1 model is thus also expected to be S-dual. We also remark that, using the untwisted dilaton and moduli fields of these constructions as spurion fields, yields soft SUSY-breaking terms which preserve finiteness even for N=0., Comment: 8 pages, LaTex

I discuss several issues concerning the use of string models as unified theories of all interactions. After a short review of gauge coupling unification in the string context, I discuss possible motivations for the construction of $SU(5)$ and $SO(10)$ String-GUTs. I describe the construction of such String-GUTs using different orbifold techniques and emphasize those properties which could be general. Although $SO(10)$ and $SU(5)$ String-GUTs are relatively easy to build, the spectrum bellow the GUT scale is in general bigger than that of the MSSM and includes colour octets and $SU(2)$ triplets. The phenomenological prospects of these theories are discussed. I then turn to discuss soft SUSY-breaking terms obtained under the assumption of dilaton/moduli dominance in SUSY-breaking string schemes. I underline the unique finiteness pr of the soft terms induced by the dilaton sector. These improved finiteness properties seem to be related to the underlying $SU(1,1)$ structure of the dilaton couplings. I conclude with an outlook and some speculations regarding $N=1$ duality., Comment: Few missprints fixed; reference added

The structure of the quark and lepton masses and mixing angles provides one of the few windows we have on the underlying physics generating the \sm. In an attempt to identify the underlying symmetry group we look for the simplest gauge extension of the SUSY standard model capable of generating the observed structure. We show that the texture structure and hierarchical form found in the (symmetric) quark and lepton mass matrices follows if one extends the gauge group of the standard model to include an horizontal $U(1)$ gauge factor, constrained by the need for anomaly cancellation. This $U(1)$ symmetry is spontaneously broken slightly below the unification/string scale leaving as its only remnant the observed structure of masses and mixings. Anomaly cancellation is possible only in the context of superstring theories via the Green Schwarz mechanism with $sin^2(\theta_W)=3/8$., Comment: 19 pages, preprint numbers OUTP-9403 and FTUAM-94/7, LaTex

I discuss some new trends in particle theory beyond the standard model. Some topics briefly covered include elecroweak baryogenesis, gauge versus non-gauge discrete symmetries, the strong CP problem, dynamical symmetry breaking scenarios, supersymmetric grand unification, new aspects in low energy supersymmetry and superstring phenomenology., Comment: 27 pages, LATEX (Plenary talk at the EPS Marseilles HEP Conference, July 1994)