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We develop a technique for counting the number of stress tensor multiplets in a 4D $\mathcal{N}=2$ SCFT. This provides a simple diagnostic for when an isolated (non-Lagrangian) SCFT is a product of two (or more) such theories. In class-S, the basic building blocks are the isolated SCFTs arising from the compactification of a 6D (2,0) theory on a 3-punctured sphere ("fixture"). We apply our technique to determine when a fixture is a product SCFT. The answer is that this phenomenon is surprisingly rare. In the low-rank $A_{N-1}$, $D_N$ theories and the $E_6$ theory studied by the first author and his collaborators, it occurs less than $1\%$ of the time. Of the 2979 fixtures in the (untwisted and twisted) $E_6$ theory, only 23 are product SCFTs. Of these, 22 were known to the original authors. The new one is a product of the ${(E_7)}_8$ Minahan-Nemeschansky theory and a new rank-2 SCFT., Comment: 14 pages, 31 figures

Although the energy spectrum of the Heisenberg spin chain on a circle defined by $H=\frac{1}{4}\sum_{k=1}^M(\sigma_k^x\sigma_{k+1}^x+\sigma_k^y\sigma_{k+1}^y +\Delta\sigma_k^z\sigma_{k+1}^z)$ is well known for any fixed $M$, the boundary conditions vary according to whether $M\in 4\mathbb{N}+r$, where $r=-1,0,1,2$, and also according to the parity of the number of overturned spins in the state, In string theory all these cases must be allowed because interactions involve a string with $M$ spins breaking into strings with $M_1, Comment: 27 pages, footnote added and typos corrected

We study, by means of numerical lattice simulations, the properties of the reconfinement phase transition taking place in trace deformed $SU(3)$ Yang-Mills theory defined on ${\mathbb{R}}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$, in which center symmetry is recovered even for small compactification radii. We show, by means of a finite size scaling analysis, that the reconfinement phase transition is first order, like the usual $SU(3)$ thermal phase transition. We then investigate two different physical phenomena, which are known to characterize the standard confinement/deconfinement phase transition, namely the condensation of thermal magnetic monopoles and the change in the localization properties of the eigenmodes of the Dirac operator. Regarding the latter, we show that the mobility edge signalling the Anderson-like transition in the Dirac spectrum vanishes as one enters the reconfined phase, as it happens in the standard confined phase. Thermal monopoles, instead, show a peculiar behavior: their density decreases going through reconfinement, at odds with the standard thermal theory; nonetheless, they condense at reconfinement, like at the usual confinement transition. The coincidence of monopole condensation and Dirac mode delocalization, even in a framework different from that of the standard confinement transition, suggests the existence of a strict link between them.

We measure the impact of nonvanishing boundary localised terms on $\Delta B=2$ transitions in five-dimensional Universal Extra Dimensional scenario where masses and coupling strengths of several interactions of Kaluza-Klein modes are significantly modified with respect to the minimal counterpart. In such scenario we estimate the Kaluza-Klein contributions of quarks, gauge bosons and charged Higgs by evaluating the one-loop box diagrams that are responsible for the $\Delta B=2$ transitions. Using the loop function (obtained from one-loop box diagrams) we determine several important elements that are involved in Wolfenstein parametrisation. Moreover, with these elements we also study the geometrical shape of unitarity triangle. Besides, we compute the quantity $\Delta M_s$ scaled by the corresponding Standard Model value. Outcomes of our theoretical predictions have been compared to the allowed ranges of the corresponding observables simultaneously. Our current analysis shows that, depending on the parameters in this scenario the lower limit on the inverse of the radius of compactification can reach to an appreciable large value ($\approx 1.48$ TeV or even higher)., Comment: A table added, some clarifying remarks added and version accepted for publication in The European Physical Journal C

Following our previous work of 1905.10745 [hep-th], 2003.11217 [hep-th], we study heterotic interpolating models D dimensionally compactified with constant background fields that include the full set of Wilson lines and radii. Focusing on the phenomenoloically viable supersymmetry restoring parameter region, we analyze the pattern of gauge symmetry enhancement and the representation of massless fermions. We obtain the set of cases with the exponentially small cosmological constant. Our analysis does not depend on non-supersymmetric endpoint models of interpolations. A part of the moduli space of interpolating models is in one-to-one correspondence with the counterpart of toroidal compactification of heterotic superstrings.

We compute the macroscopic entropy of the supersymmetric rotating dyonic strings carrying linear momentum in 6D (1,0) supergravity with curvature squared corrections. Our calculation is based on Sen's entropy function formalism applied to the near-horizon geometry of the string solution taking the form of an extremal BTZ$\times S^3$. The final entropy formula states that the two independent supersymmetric completions of Riemann tensor squared contribute equally to the entropy. A further $S^3$ compactification of the 6D theory results in a matter coupled 3D supergravity model in which the quantization condition of the SU(2)$_R$ Chern-Simons level implies the horizon value of the dilaton is not modified by higher derivative interactions beyond supersymmetric curvature squared terms., Comment: 20 pages, discussions added

In flux compactifications of type IIB string theory with D3 and seven-branes, the negative induced D3 charge localized on seven-branes leads to an apparently pathological profile of the metric sufficiently close to the source. With the volume modulus stabilized in a KKLT de Sitter vacuum this pathological region takes over a significant part of the entire compactification, threatening to spoil the KKLT effective field theory. In this paper we employ the Seiberg-Witten solution of pure $SU(N)$ super Yang-Mills theory to argue that wrapped seven-branes can be thought of as bound states of more microscopic exotic branes. We argue that the low-energy worldvolume dynamics of a stack of $n$ such exotic branes is given by the $(A_1,A_{n-1})$ Argyres-Douglas theory. Moreover, the splitting of the perturbative (in $\alpha'$) seven-brane into its constituent branes at the non-perturbative level resolves the apparently pathological region close to the seven-brane and replaces it with a region of $\mathcal{O}(1)$ Einstein frame volume. While this region generically takes up an $\mathcal{O}(1)$ fraction of the compactification in a KKLT de Sitter vacuum we argue that a small flux superpotential \textit{dynamically} ensures that the 4d effective field theory of KKLT remains valid nevertheless., Comment: 42 pages, 19 figures, 1 appendix; v2: references added, minor corrections; v3: monodromies corrected, reference added; v4: matches version published in JHEP

We obtain the Hamiltonian formulation of the 11D Supermembrane theory non-trivially compactified on a twice-punctured torus times a 9D Minkowski space-time. It corresponds to a M2-brane formulated in 11D space with ten non-compact dimensions. The critical points like the poles and the zeros of the fields describing the embedding of the Supermembrane in the target space are treated rigorously. The non-trivial compactification generates non-trivial mass terms appearing in the bosonic potential, which dominate the full supersymmetric potential and should render the spectrum of the (regularized) Supermembrane discrete with finite multiplicity. The behaviour of the fields around the punctures generates a cosmological term in the Hamiltonian of the theory. The massive supermembrane can also be seen as a nontrivial uplift of a supermembrane torus bundle with parabolic monodromy in $M_9\times T^2$. The moduli of the theory is the one associated with the punctured torus, hence it keeps all the nontriviality of the torus moduli even after the decompactification process to ten noncompact dimensions. The formulation of the theory on a punctured torus bundle is characterized by the $(1,1)-Knots$ associated with the monodromies., 25 pages, 5 figures

We determine the 1-form symmetry group for any 4d N = 2 class S theory constructed by compactifying a 6d N=(2,0) SCFT on a Riemann surface with arbitrary regular untwisted and twisted punctures. The 6d theory has a group of mutually non-local dimension-2 surface operators, modulo screening. Compactifying these surface operators leads to a group of mutually non-local line operators in 4d, modulo screening and flavor charges. Complete specification of a 4d theory arising from such a compactification requires a choice of a maximal subgroup of mutually local line operators, and the 1-form symmetry group of the chosen 4d theory is identified as the Pontryagin dual of this maximal subgroup. We also comment on how to generalize our results to compactifications involving irregular punctures. Finally, to complement the analysis from 6d, we derive the 1-form symmetry from a Type IIB realization of class S theories., Comment: 62 pages, 43 TikZ figures; v2: Important typos corrected

We analyze the stability of four-dimensional de Sitter vacua constructed by compactifying massive Type IIA supergravity in the presence of two O8 sources [1]. When embedded in String Theory the first source has a clear interpretation as an O8$_-$ plane, but the second one could correspond to either an O8$_+$ plane or to an O8$_-$ plane with 16 D8-branes on top. We find that this latter solution has a tachyonic instability, corresponding to the D8-branes moving away from the O8$_-$ plane. We comment on the possible ways of distinguishing between these sources., 19 pages and 4 figures. Version 2: references added

We study possibilities to realize a nonvanishing finite Wilson line (WL) scalar mass in flux compactification. Generalizing loop integrals in the quantum correction to WL mass at one-loop, we derive the conditions for the loop integrals and mode sums in one-loop corrections to WL scalar mass to be finite. We further guess and classify the four-point and three-point interaction terms satisfying these conditions. As an illustration, the nonvanishing finite WL scalar mass is explicitly shown in a six dimensional scalar QED by diagrammatic computation and effective potential analysis. This is the first example of finite WL scalar mass in flux compactification., Comment: 21 pages, 1 figure, final version to appear in JHEP

This is the first of a series of three papers on open string field theories based on Witten star product deformed with a gauge invariant open/closed coupling. This de- formation is a tree-level tadpole which destabilizes the initial perturbative vacuum. We discuss the existence of vacuum-shift solutions which cancel the tadpole and represent a new configuration where the initial D-brane system has adapted to the change in the closed string background. As an example we consider the bulk deformation which changes the compactification radius and, to first order in the deformation, we reproduce the shift in the mass of the open string KK modes from the new kinetic operator after the vacuum shift. We also discuss the possibility of taming closed string degenerations with the open string propagator in the simplest amplitude corresponding to two closed strings off a disk., Journal of High Energy Physics, 2021 (9), ISSN:1126-6708, ISSN:1029-8479

According to modern quantum physics, at the microlevel, the dimension of space-time is \(\ge \)11; we only observe 4 dimensions because the others are compactified: the size along each of the other dimensions is much smaller than the macroscale. There is no universally accepted explanation of why exactly 4 dimensions remain at the microscopic level. A natural suggestion is: maybe there is no fundamental reason why exactly 4 dimensions should remain, maybe when we go to even larger scales, some of the 4 dimensions will be compactified as well? In this paper, we explore the consequences of the compactification suggestion, and we show that—on the qualitative level—these consequences have actually been already observed: as superclusters and as evidence that is usually interpreted as justifying dark matter. Thus, we get a new possible explanation of both superclusters and dark matter evidence—via dimension compactification.

In this paper by using the Poincaré compactification of ℝ3 we make a global analysis of the model xʹ = ax + y + yz, yʹ = x–ay + bxz, zʹ = cz–bxy. In particular we give the complete description of its dynamics on the infinity sphere. For a + c = 0 or b = 1 this system has invariants. For these values of the parameters we provide the global phase portrait of the system in the Poincaré ball. We also describe the α and ω-limit sets of its orbits in the Poincaré ball. © 2020, © 2020 Taylor & Francis.

Braneworld scenarios appear in dynamical string tension theories, where string tension is positive between two surfaces separated by a short distance and at the two surfaces themselves the string tensions become infinite, therefore producing an effective confinement of the strings and therefore of all matter and gravity to the space between these to surfaces. The specific model studied is in the context of the modified measure formulation the string where tension appear as an additional dynamical degree of freedom and these tensions are not universal, but rather each string generates its own tension, which can have a different value for each string. We consider a new background field that can couple to these strings, the tension scalar is capable then of changing locally along the world sheet and then the value of the tension of the string object changes accordingly along the world sheet. Sting tension appears dynamically and each string tension has a characteristic constant of integration that appears as a consequence of the dynamical tension generation . When many types of strings probing the same region of space are considered this tension scalar is constrained by the requirement of quantum conformal invariance. For the case of two types of strings probing the same region of space with different dynamically generated tensions (characterized by different constants of integration) , there are two different metrics, associated to the different strings, that have to satisfy vacuum Einsteins equations and the consistency of these two Einsteins equations determine that the tension field behaves. The two metrics are flat space in Minkowshi space and flat space after a special conformal transformation, then the strings are confined inside a light like Segment or alternatively as expanding Braneworlds where the strings are confined between two expanding bubbles., Comment: 17 pages. References added. This version has been accepted for publication in European Physics Journal C. arXiv admin note: substantial text overlap with arXiv:2105.02279, arXiv:2104.08875

Dark photons and mirror matter are well-motivated dark matter candidates. It is possible that both of them arose during the compactification and symmetry breaking scenario of the heterotic $E_8\times E_8$ string theory and are related to each other. In this case, dark photons can become a natural portal into the mirror world. Unfortunately, the expected magnitude of the induced interactions of ordinary matter with mirror matter is too small to be of phenomenological interest., Comment: 9 pages, no figures, revtex4, version to be published in Modern Physics Letters A

Among the allowed representations of extended supersymmetry in six dimensions there are exotic chiral multiplets that, instead of a graviton, contain mixed-symmetry spin-2 tensor fields. Notably, an $\mathcal{N}=(4,0)$ multiplet has a four index exotic graviton and it was conjectured that an interacting theory based on this multiplet could arise as a strong coupling limit of M theory compactified on $T^6$. We present an algebraic study of these multiplets and their possible embedding into the framework of exceptional field theory, finding in particular that the six-dimensional momenta do not correspond to a conventional spacetime section. When compactified on a circle, the six-dimensional multiplets give rise to the same degrees of freedom as five-dimensional supergravity theories with the same number of supersymmetries. However, by considering anomalies (computed using the product multiplets construction) and the generation of Chern-Simons couplings, we find reason to doubt that their dynamics will agree with the five-dimensional gravity theories. We propose an alternative picture, similar to F-theory, in which particular fixed-volume $T^3$-fibered spacetimes play a central role, suggesting that only on compactification to three-dimensions will one make contact with the dynamics of supergravity., 77 pages

This article reports on the survey talk 'Hilbert's Sixteenth Problem for Liénard equations,' given by the author at the Oberwolfach Mini-Workshop 'Algebraic and Analytic Techniques for Polynomial Vector Fields.' It is written in a way that it is accessible to a public with heterogeneous mathematical background. The article reviews recent developments and techniques used in the study of Hilbert's 16th problem where the main focus is put on the subclass of polynomial vector fields derived from the Liérd equations.

The existence of a field-theoretic target space action and its fundamental relation to the worldsheet definition of the theory has already been discussed in the context of the bosonic string. All that was said there remains true. In particular, there are always the 10d graviton and B2 field, coupling to the worldsheet (except in the case of the unoriented type I string, where it falls victim to the projection taking us from type IIB to type I). There is also always the dilaton, governing the convergence of perturbation theory. Together, dilaton, graviton and B2 form the NS–NS sector (see above). As a novelty, one has the Cp+1 (or RR) form fields and the corresponding Dp-branes. These are dynamical objects, just like the string itself, but with different dimensionalities and (at weak string coupling) larger tensions. This analysis would be slightly different in the heterotic case, where there are no C-forms but rather gauge fields. Crucially, there are now also fermionic partners for all the fields above.

By dimensional reduction of the Lovelock Lagrangian, effective four-dimensional field equations and expressions for the cosmological and gravitational constants are obtained. A cosmological model is discussed with the n-torus as internal space., Comment: 11 pages, a typo in equation (3.17) of the original publication has been corrected

We study the integrable bi-Yang-Baxter deformation of the $SU(2)$ principal chiral model (PCM) and its finite action uniton solutions. Under an adiabatic compactification on an $S^1$, we obtain a quantum mechanics with an elliptic Lam\'e-like potential. We perform a perturbative calculation of the ground state energy in this quantum mechanics to large orders obtaining an asymptotic series. Using the Borel-Pad\'e technique, we determine the expected locations of branch cuts in the Borel plane of the perturbative series and show that they match the values of the uniton actions. Therefore, we can match the non-perturbative contributions to the energy with the uniton solutions which fractionate upon adiabatic compactification. An off-shoot of the WKB analysis, is to identify the quadratic differential of this deformed PCM with that of an $\mathcal{N}=2$ Seiberg-Witten theory. This can be done either as an $N_f=4$ $SU(2)$ theory or as an elliptic quiver $SU(2)\times SU(2)$ theory. The mass parameters of the gauge theory are given by the deformation parameters of the PCM., Comment: 50 pages, 18 figures

We study surface defects in 4d N = 1 S U ( N ) superconformal gauge theories of class S k obtained from the 6d (1,0) theories of type A N − 1 , which are worldvolume theories on N M5-branes at C 2 / Z k singularities, compactified on Riemann surfaces with punctures. We evaluate the superconformal indices with surface defects for the orbifold of linear quiver gauge theories by two methods. First we apply a method based on Riemann surface description and obtain the superconformal index of the theories in the presence of surface defects labelled by arbitrary symmetric representations of s u ( N ) . Then we propose another description for the same surface defects, which involves 4d-2d coupled systems, by identifying which 2d N = ( 0 , 2 ) theories should be coupled. We compute the index of the 4d-2d systems and reproduce the results obtained from the first method. Finally we study the 2d TQFT structure of the index for class S k theories by obtaining several eigenfunctions and eigenvalues of the difference operators that capture the surface defects and checking their relation.

Chaotic attractors with no equilibria, with an unstable node, and with stable node-focus are presented in this paper. The conservative solutions are investigated by the semianalytical and seminumerical method. Furthermore, multiple coexisting attractors are investigated, and circuit is carried out. To study the system’s global structure, dynamics at infinity for this new chaotic system are studied using Poincaré compactification of polynomial vector fields in R 3 . Meanwhile, the dynamics near the infinity of the singularities are obtained by reducing the system’s dimensions on a Poincaré ball. The averaging theory analyzes the periodic solution’s stability or instability that bifurcates from Hopf-zero bifurcation.

We further study the cancellation of the one-loop corrections to the scalar mass in a six dimensional SU(2) gauge theory with higher dimensional operators, which is compactified on a torus with magnetic flux. Higher dimensional operators also contribute to the corrections to the scalar mass nontrivially. We explicitly show by the diagrammatic calculations that the corrections are exactly cancelled even with the leading terms of the higher dimensional operators., 29 pages, 4 figures

We consider the multiple Calaby-Yau (CY) mirror phenomenon which appears in Berglund-H\"ubsch-Krawitz (BHK) mirror symmetry. We show that for any pair of Calabi--Yau orbifolds that are BHK mirrors of a loop--chain type pair of Calabi--Yau manifolds in the same weighted projective space the periods of the holomorphic nonvanishing form coincide., Comment: Some important changes of the content and title, typos fixed

Tiny values for gauge couplings of dark photons allow to suppress their kinetic mixing with ordinary photons. We point out that the Weak Gravity Conjecture predicts consequently low ultraviolet cut-offs where new degrees of freedom might appear. In particular, a mixing angle of $\mathcal{O}(10^{-15})$, required in order to fit the excess reported by XENON1T, corresponds to new physics below $\mathcal{O}(100)$ TeV, thus accessible at a Future Circular Collider. We show that possible realizations are provided by compactifications with six large extra dimensions and a string scale of order $\mathcal{O}(100)$ TeV., Comment: 9 pages. A few comments and references improved. This version matches the one published

We study the possibility of realizing scale-separated type IIB Anti-de Sitter and de Sitter compactifications within a controlled effective field theory regime defined by low-energy and large (but scale-separated) compactification volume. The approach we use views effective theories as truncations of the full quantum equations of motion expanded in a trans-series around this asymptotic regime. By studying the scalings of all possible perturbative and non-perturbative corrections we identify the effects that have the right scaling to allow for the desired solutions. In the case of Anti-de Sitter, we find agreement with KKLT-type scenarios, and argue that non-perturbative brane-instantons wrapping four-cycles (or similarly scaling effects) are essentially the only ingredient that allows for scale separated solutions. We also comment on the relation of these results to the AdS swampland conjectures. For the de Sitter case we find that we are forced to introduce an infinite number of relatively unsuppressed corrections to the equations of motion, leading to a breakdown of effective theory. This suggests that if de Sitter vacua exist in the string landscape, they should not be thought of as residing within the same effective theory as the AdS or Minkowski compactifications, but rather as defining a separate asymptotic regime, presumably related to the others by a duality transformation., Comment: 24 pages, v2 changes to the scaling analysis in section 3.4, references added

We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a toric Calabi-Yau threefold, the D-branes wrapping holomorphic cycles represent the BPS states, and the fixed points of the moduli spaces of BPS states are described by statistical configurations of crystal melting. Our algebras are "bootstrapped" from the molten crystal configurations, hence they act on the BPS states. We discuss the truncation of the algebra and its relation with D4-branes. We illustrate our results in many examples, with and without compact $4$-cycles., 137 pages, 34 figures. v3: matches with JHEP version; added two footnotes on page 18 and page 114 to clarify the issue of the sign choice in the bond factors

We propose a top down construction for Jackiw-Teitelboim (JT) gravity using compactification of D=5 gravity theories in the presence of Abelian [U(1)] as well as SU(2) Yang-Mills fields. The background solutions corresponding to the D=2 model have been obtained in the perturbative regime of the theory where the corrections have been estimated over the uncharged JT solutions while treating the gauge couplings as the parameters of the expansion. Our analysis reveals the existence of two classes of solutions, namely, (i) the interpolating vacuum solution with AdS2 in the IR and Lifshitz2 in the UV (which serves as the thermal radiation background for our analysis) and (ii) the charged 2D black hole solution exhibiting Lifshitz2 asymptotics. The analysis on thermal stability reveals the onset of a first-order phase transition at T∼T0 such that for TT0), an emerging globally stable black-hole-dominated phase has been observed which clearly indicates the onset of a Hawking-Page transition in 2D gravity models.

We construct global orientifold limits of singular $F$-theory vacua whose associated gauge groups are SO(3), SO(5), SO(6), $F_4$, SU(4), and Spin(7). For each limit we show a universal tadpole relation is satisfied, which is a homological identity whose dimension-zero component encodes the matching of the D3 charge between each $F$-theory compactification and its orientifold limit. While for smooth $F$-theory compactifications which admit global orientifold limits the contribution to the associated universal tadpole relation comes from its Chern class, we show that for all singular $F$-theory compactifications under consideration, the contribution to the universal tadpole relation comes from its \emph{stringy} Chern class., No figures