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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: 54 pages + Appendix, 17 figures, 2 tables

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., v2: minor changes and typos corrected. 79 pages + Appendices, 11 figures, 8 tables

In this work we obtain classical solutions of the bosonic sector of the supermembrane theory with two-form fluxes associated to a quantized constant $C_{\pm}$ background. This theory satisfies a flux condition on the worldvolume that induces monopoles over it. Classically it is stable as it does not contain string-like spikes with zero energy in distinction with the general case. At quantum level the bosonic membrane has a purely discrete spectrum but the relevance is that the same property holds for its supersymmetric spectrum. We find for this theory spinning membrane solutions, some of them including the presence of a non-vanishing symplectic gauge connection defined on its worldvolume in different approximations. By using the duality found between this theory and the so-called supermembrane with central charges, rotating membrane solutions found in that case, are also solutions of the M2-brane with $C_{\pm}$ fluxes. We generalize this result to other embeddings. We find new distinctive rotating membrane solutions, some of them including the presence of a non-vanishing symplectic gauge connection defined on its worldvolume. We obtain numerical and analytical solutions in different approximations characterizing the dynamics of the membrane with fluxes $C_{\pm}$ for different ans\"atze of the dynamical degrees of freedom. Finally we discuss the physical admissibility of some of these ans\"atze to model the components of the symplectic gauge field., Comment: Some clarifications added to section 2 and the discussion session has been enriched. Some references added. Results unchanged. Some change letter size. Latex, 33 pages, 5 figures. Accepted in JHEP

International audience; 5d Superconformal Field Theories (SCFTs) are intrinsically strongly-coupled UV fixed points, whose realization hinges on string theoretic methods: they can be constructed by compactifying M-theory on local Calabi-Yau threefold singularities or alternatively from the world-volume of 5-brane-webs in type IIB string theory. There is a correspondence between 5-brane-webs and toric Calabi-Yau threefolds, however this breaks down when multiple 5-branes are allowed to end on a single 7-brane. In this paper, we extend this connection and provide a geometric realization of brane configurations including 7-branes. A web with 7-branes defines a so-called generalized toric polygon (GTP), which corresponds to combinatorial data that is obtained by removing vertices along external edges of a toric polygon. We identify the geometries associated to GTPs as non-toric deformations of toric Calabi-Yau threefolds and provide a precise, algebraic description of the geometry, when 7-branes are introduced along a single edge. The key ingredients in our analysis are T-branes in a type IIA frame, which includes D6-branes. We show that performing Hanany-Witten moves for the 7-branes on the type IIB side corresponds to switching on semisimple vacuum expectation values on the worldvolume of D6-branes, which in turn uplifts to complex structure deformations of the Calabi-Yau geometries. We test the proposal by computing the crepant resolutions of the deformed geometries, thereby checking consistency with the expected properties of the SCFTs.

We construct large families of supergravity solutions that are asymptotic to AdS$_2$ and terminate with a cap that is singular in two dimensions but smooth in higher dimensions. These solutions break supersymmetry and conformal invariance. We list arguments suggesting that they correspond to finite-energy excitations in empty AdS$_2$ that back-react on the geometry by inducing non-trivial bubbling topology. They are constructed from the novel technique associated with the Ernst formalism for AdS$_D\times\mathcal{C}$ solitons in supergravity \cite{Bah:2022pdn}. The technique is applied to $D=2$ in M-theory with $\mathcal{C}=\,$S$^3\times$T$^6$. The directions of $\mathcal{C}$ degenerate smoothly as a chain of bolts which ends the spacetime in the IR and generates non-supersymmetric bubbles supported by M2-brane flux. Some specific solutions have ``flat'' directions where the sizes of their bubbles are totally unconstrained and can be arbitrarily tuned while the asymptotics remains fixed. The solitons should correspond to regular non-supersymmetric states of a holographically dual CFT$_1$., Comment: 46 pages, 15 figures, 3 appendices. v2 published version: minor corrections + section about energy of the solutions. arXiv admin note: text overlap with arXiv:2210.06483

We construct supersymmetric $AdS_5\times \Sigma$ solutions of $D=7$ gauged supergravity, where $\Sigma$ is a two-dimensional orbifold known as a spindle. These uplift on $S^4$ to solutions of $D=11$ supergravity which have orbifold singularites. We argue that the solutions are dual to $d=4$, $\mathcal{N}=1$ SCFTs that arise from $N$ M5-branes wrapped on a spindle, embedded as a holomorphic curve inside a Calabi-Yau three-fold. In contrast to the usual topological twist solutions, the superconformal R-symmetry mixes with the isometry of the spindle in the IR, and we verify this via a field theory calculation, as well as reproducing the gravity formula for the central charge., Comment: 25 pages. Very minor change, published version

We analyze conditions for a tri-vector deformation of a supergravity background to preserve some supersymmetry. Working in the formalism of the SL(5) exceptional field theory, we present its supersymmetry transformations and introduce an additional USp(4) transformation to stay in the supergravity frame. This transformation acts on local indices and deforms BPS equations of exceptional field theory. The requirement for the deformation to vanish is the desired condition. The condition is shown to be consistent with previous results on bi-vector deformations.

We describe three previously unnoticed components of the moduli space of minimally supersymmetric string theories in $d\geq 7$, describing in some detail their spectrum and duality properties. We find a new component in nine and eight dimensions, and two additional ones in seven dimensions. These theories were originally discovered in a bottom-up classification of possible F/M-theory singularity freezing patterns in the K3 lattice, described in a companion paper. The 9d/8d component can be understood as F/M-theory on a twisted fibration of the Klein bottle over a circle, while the new seven-dimensional components are described as IIB on Bieberbach manifolds with a duality bundle and RR-NSNS backgrounds turned on. All the new components can be obtained from previously known theories by turning on certain discrete theta angles; however, the spectrum of massive objects is very different, and most strikingly, they feature an incomplete lattice of BPS strings, showing that string BPS completeness is not true in general even with sixteen supercharges. In all cases we find non-BPS representatives for each value of the charge, so the Completeness Principle is satisfied. We also analyze analogous theta angles in nonsupersymmetric string theories, and provide a detailed explanation of why the Type I discrete $\theta$ angle proposed in 1304.1551 is unphysical, using this to clarify certain non-perturbative phenomena in $O8$ planes., Comment: 45 pages + references, 4 figures, and 3 new string theories

In this note we consider smooth elliptic Calabi-Yau four-folds whose fiber ceases to be flat over compact Riemann surfaces of genus $g$ in the base. These non-flat fibers contribute Kaehler moduli to the four-fold but also add to the three-form cohomology for $g>0$. In F-/M-theory these sectors are to be interpreted as compactifications of six/five dimensional $\mathcal{N}=(1,0)$ superconformal matter theories. The three-form cohomology leads to additional chiral singlets proportional to the dimension of five dimensional Coulomb branch of those sectors. We construct explicit examples for E-string theories as well as higher rank cases. For the E-string theories we further investigate conifold transitions that remove those non-flat fibers. First, we show how non-flat fibers can be deformed from curves down to isolated points in the base. This removes the chiral singlet of the three-forms and leads to non-perturbative four-point couplings among matter fields which can be understood as remnants of the former E-string. Alternatively, the non-flat fibers can be avoided by performing birational base changes, analogous to 6D tensor branches. For compact bases these transitions alternate all Hodge numbers but leave the Euler number invariant., 28 pages, 5 pages appendix, 6 figures, 2 tables

We construct a pseudo-Lagrangian that is invariant under rigid $E_{11}$ and transforms as a density under $E_{11}$ generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on $E_{11}$ exceptional field theory and the inclusion of constrained fields that transform in an indecomposable $E_{11}$-representation together with the $E_{11}$ coset fields. We show that, in combination with gauge-invariant and $E_{11}$-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condition. For another choice, we reobtain the $E_8$ exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the $E_{10}$ sigma model., Minor corrections, accepted for publication in JHEP

We present a six-dimensional $\mathcal{N}=(1,0)$ supersymmetric higher gauge theory in which self-duality is consistently implemented by physically trivial additional fields. The action contains both $\mathcal{N}=(1,0)$ tensor and vector multiplets and is non-trivially interacting. The tensor multiplet part is loosely related to a recently proposed action by Sen that leads to on-shell self-duality in an elegant way. As we also show, Sen's action finds a very natural and direct interpretation from a homotopy algebraic perspective., 29 pages, typos fixed, clarifications added, published version

We study the non-linear structure of Type IIB eight-derivative couplings involving the metric and the complexified three-form $G_3$. We show that, at the level of five-point string amplitudes, the kinematics in the maximally R-symmetry-violating sector is fully matched by standard superspace integrals and by superparticle amplitudes in M-theory on a two-torus. The latter approach is used to determine the complete effective action in this sector and to verify its invariance under SL$(2,\mathbb{Z})$ duality. We further comment on the general structure of the higher-point kinematics. Compactifications to lower dimensions provide both tests for our results and the arena for their applications. We verify that K3 reductions are fully consistent with the constraints of six-dimensional supersymmetry, and derive the four-dimensional flux scalar potential and axion kinetic terms at order $(\alpha^{\prime})^{3}$ in Calabi-Yau threefold reductions., Comment: 34 pages plus appendices

D3 branes in the vicinity of an E6, E7, or E8 stack of 7-branes in flat space are known to host at low energy a famous class of strongly-coupled N = 2 superconformal field theories featuring exceptional global symmetry. What if, instead, the 7-branes wrap an orbifold? We give a systematic characterization of such theories in the case of C2/Zn, and determine their main properties, like global symmetries, spectra of Coulomb-branch operators, and patterns of Higgs-branch flows. We put forward a set of rules to construct their magnetic quivers, which directly generalize what happens in the perturbative case, and later derive them using the duality with M5 branes probing M9 walls., Comment: 53 pages and many figures

We study graviton scattering on $AdS_4\times S^7$, which is dual to the stress tensor multiplet four-point function in the maximally supersymmetric 3d $U(N)_1\times U(N)_{-1}$ ABJM theory. We compute 1-loop corrections to this holographic correlator coming from Witten diagrams with supergravity $R$ and higher derivative $R^4$ vertices, up to contact term ambiguities, and find that the flat space limit matches the corresponding terms in the 11d M-theory S-matrix. We then use supersymmetric localization to show that all the 1-loop contact terms vanish, as was previously observed for the $AdS_4\times S^7/\mathbb{Z}_2$ theory dual to $U(N)_2\times U(N)_{-2}$ ABJM. Finally, we use the recent localization results of Gaiotto and Abajian, as inspired by twisted M-theory, to compute all the short OPE coefficients in correlators of the stress tensor multiplet and the next lowest half-BPS operator, which we find saturate the bootstrap bounds on these mixed correlators for all $N$., 20 pages, 2 figures, sequel to arXiv:2107.10274, v2 submitted to JHEP

The dynamics of chiral p-forms can be captured by a lower-dimensional parity-violating action motivated by a Kaluza-Klein reduction on a circle. The massless modes are (p-1)-forms with standard kinetic terms and Chern-Simons couplings to the Kaluza-Klein vector of the background metric. The massive modes are p-forms charged under the Kaluza-Klein vector and admit parity-odd first-order kinetic terms. Gauge invariance is implemented by a Stueckelberg-like mechanism using (p-1)-forms. A Chern-Simons term for the Kaluza-Klein vector is generated at one loop by massive p-form modes. These findings are shown to be consistent with anomalies and supersymmetry for six-dimensional supergravity theories with chiral tensor multiplets., Comment: 4 pages, 1 figure

We study circle compactifications of 6d superconformal field theories giving rise to 5d rank 1 and rank 2 Kaluza-Klein theories. We realise the resulting theories as M-theory compactifications on local Calabi-Yau 3-folds and match the prepotentials from geometry and field theory. One novelty in our approach is that we include explicit dependence on bare gauge couplings and mass parameters in the description which in turn leads to an accurate parametrisation of the prepotential including all parameters of the field theory. We find that the resulting geometries admit "fibre-base" duality which relates their six-dimensional origin with the purely five-dimensional quantum field theory interpretation. The fibre-base duality is realised simply by swapping base and fibre curves of compact surfaces in the local Calabi-Yau which can be viewed as the total space of the anti-canonical bundle over such surfaces. Our results show that such swappings precisely occur for surfaces with a zero self-intersection of the base curve and result in an exchange of the 6d and 5d pictures., Comment: v3: 60 pages, several typos corrected, matches JHEP version

We classify the necessary and sufficient conditions to obtain the near-horizon geometry of extremal supersymmetric rotating black holes embedded in 11d supergravity. Such rotating black holes admit an AdS$_2$ near-horizon geometry which is fibered by the transverse spacetime directions. Despite their clear interest to understanding the entropy of rotating black holes, these solutions have evaded all previous supersymmetric classification programs due to the non-trivial fibration structure. In this paper we allow for the most general fibration over AdS$_2$ with a flux configuration permitting rotating M2-branes. Using G-structure techniques we rewrite the conditions for supersymmetry in terms of differential equations on an eight-dimensional balanced space. The 9d compact internal space is a U$(1)$-fibration over this 8d base. The geometry is constrained by a master equation reminiscent of the one found in the non-rotating case. We give a Lagrangian from which the equations of motion may be derived, and show how the asymptotically AdS$_4$ electrically charged Kerr-Newman black hole in 4d $\mathcal{N}=2$ supergravity is embedded in the classification. In addition, we present the conditions for the near-horizon geometry of rotating black strings in Type IIB by using dualities with the 11d setup., Comment: 31 pages plus appendix

We calculate the superconformal indices of a class of six-dimensional ${\cal N}=(1,0)$ superconformal field theories realized on M5-branes at $\mathbb{C}^2/\mathbb{Z}_k$ singularity by using the method developed in previous works of the authors and collaborators. We use the AdS/CFT correspondence, and finite $N$ corrections are included as the contribution of M2-branes wrapped on two-cycles in $S^4/\mathbb{Z}_k$. We confirm that the indices are consistent with the expected flavor symmetries., 18 pages, 1 figure; ver2: references added; ver3: references added, version accepted for publication in JHEP

M-theory on local $G_2$-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered $G_2$-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum., 70 pages, 16 figures, JHEP version

The full 6d Hopf-Wess-Zumino term in the action functional for the M5-brane is anomalous as traditionally defined. What has been missing is a condition implying the higher analogue of level quantization familiar from the 2d Wess-Zumino term. We prove that the anomaly cancellation condition is implied by the hypothesis that the C-field is charge-quantized in twisted Cohomotopy theory. The proof follows by a twisted/parametrized generalization of the Hopf invariant, after identifying the full 6d Hopf-Wess-Zumino term with a twisted homotopy Whitehead integral formula, which we establish., 22 pages; v2 fixes a missing theta7-summand in intermediate formulas and has two remarks added, for clarification; v3 fixes typos and makes the slicing over the homotopy fiber space of chi_8 more explicit

We construct purely non-perturbative anti-de Sitter vacua in string theory which, on uplifting to a de Sitter (dS) one, have a decay time many orders of magnitude smaller than those of standard constructions, such as the KKLT and LVS scenarios. By virtue of being constructed purely from non-perturbative terms, these vacua avoids certain obstructions plaguing other constructions of dS in string theory. This results in a new class of phenomenological dS vacua in string theory with novel distinctive characteristics such as having two maxima. After examining whether these uplifted dS vacua obey the TCC, we revisit some old problems of realization of dS space as a vacuum. We find that not only is it phenomenologically hard to construct TCC-compatible vacua, but also inherent temporal dependences of the degrees of freedom generically arise in such constructions, amongst other issues. This reinforces the idea that dS, if it exists in string theory, should be a Glauber-Sudarshan state and not a vacuum., 41 pages, 2 figures; references added

We explore BPS quivers for D=5 theories, compactified on a circle and geometrically engineered over local Calabi-Yau 3-folds, for which many of known machineries leading to (refined) indices fail due to the fine-tuning of the superpotential. For Abelian quivers, the counting reduces to a geometric one, but the technically challenging $L^2$ cohomology proved to be essential for sensible BPS spectra. We offer a mathematical theorem to remedy the difficulty, but for non-Abelian quivers, the cohomology approach itself fails because the relevant wavefunctions are inherently gauge-theoretical. For the Cartan part of gauge multiplets, which suffers no wall-crossing, we resort to the D0 picture and reconstruct entire KK towers. We also perform numerical checks using a multi-center Coulombic routine, with a simple hypothesis on the quiver invariants, and extend this to electric BPS states in the weak coupling chamber. We close with a comment on known Donaldson-Thomas invariants and on how $L^2$ index might be read off from these., 49 pages, 11 figures, 1 table, more references added in ver.2

We study M-theory compactified on twisted 7-tori with $G_2$-holonomy. The effective 4d supergravity has 7 chiral multiplets, each with a unit logarithmic K\"ahler potential. We propose octonion, Fano plane based superpotentials, codifying the error correcting Hamming (7,4) code. The corresponding 7-moduli models have Minkowski vacua with one flat direction. We also propose superpotentials based on octonions/error correcting codes for Minkowski vacua models with two flat directions. We update phenomenological $\alpha$-attractor models of inflation with $3\alpha=7,6,5,4,3,1$, based on inflation along these flat directions. These inflationary models reproduce the benchmark targets for detecting B-modes, predicting 7 different values of $r = 12\alpha/N_{e}^{2}$ in the range $10^{-2}\gtrsim r \gtrsim 10^{-3}$, to be explored by future cosmological observations., Comment: 63 pages, 25 figures, v2: comments added, typos fixed, v3: improved formulation presented in Sec.7 and refs added. The new formulation does not change inflationary predictions, but the potentials for decoupled heavy modes are simplified compared with the ones in the previous versions

We classify rank zero 5d SCFTs geometrically engineered from M-theory on quasi-homogeneous compound Du Val isolated threefold singularities. For all such theories, we characterize the Higgs Branch, by computing the dimension, the continuous and discrete symmetry groups, as well as more refined details such as the charges of the hypermultiplets under these groups. We derive these data by means of a gauge-theoretic method, that we have recently introduced, based on establishing a correspondence between an adjoint Higgs field and the M-theory geometry. As a byproduct, this further allows us to construct several T-brane backgrounds, that yield inequivalent 5d spectra but are associated with the same geometry., 49 pages + appendices

The conifold is a basic example of a noncompact Calabi-Yau threefold that admits a simple flop, and in M-theory, gives rise to a 5d hypermultiplet at low energies, realized by an M2-brane wrapped on the vanishing sphere. We develop a novel gauge-theoretic method to construct new classes of examples that generalize the simple flop to so-called length ℓ = 1, . . . , 6. The method allows us to naturally read off the Gopakumar-Vafa invariants. Although they share similar properties to the beloved conifold, these threefolds are expected to admit M2-bound states of higher degree ℓ. We demonstrate this through our computations of the GV invariants. Furthermore we characterize the associated Higgs branches by computing their dimensions and flavor groups. With our techniques we extract more refined data such as the charges of the hypers under the flavor group.

Vacuum compactifications may suffer from instabilities under small perturbations or tunnel effects; both are difficult to analyze. In this paper we consider the issue from a higher-dimensional perspective. We first look at how stability works for supersymmetric vacua, where it is widely expected to hold. We first show that the nucleation of brane bubbles in type II AdS compactifications is forbidden in the probe approximation by a simple argument involving pure spinors and calibrations. We then adapt familiar positive-energy theorems directly to M-theory and type II supergravity, rather than to their effective lower-dimensional reductions, also showing how to consistently include localised sources. We finally initiate an analysis of how these arguments might be extended to non-supersymmetric vacua. In M-theory, at the lower-derivative level, we find that the most natural modifications fail to stabilize the skew-whiffed and Englert vacua., Comment: v2: References added, published version, 32+16 pages

We characterize the integral cohomology and the rational homotopy type of the maximal Borel-equivariantization of the combined Hopf/twistor fibration, and find that subtle relations satisfied by the cohomology generators are just those that govern Horava-Witten's proposal for the extension of the Green-Schwarz mechanism from heterotic string theory to heterotic M-theory. We discuss how this squares with the Hypothesis H that the elusive mathematical foundation of M-theory is based on charge quantization in J-twisted Cohomotopy theory., 30 pages; v2: exposition of real homotopy theory slightly expanded, final version published in RMP

A superpotential deformation that is cubic in one of the chiral superfields of ABJM makes the latter theory flow into a new, ${\cal N}=2$ superconformal phase. This is holographically dual to a warped $\textrm{AdS}_4 \times_w S^7$ solution of M-theory equipped with a squashed and stretched metric on $S^7$. We determine the spectrum of spin-2 operators of the cubic deformation at low energies by computing the spectrum of Kaluza-Klein (KK) gravitons over the dual AdS$_4$ solution. We calculate, numerically, the complete graviton spectrum and, analytically, the spectrum of gravitons that belong to short multiplets. We also use group theory to assess the structure of the full KK spectrum, and conclude that ${\cal N}=2$ supermultiplets cannot be allocated KK level by KK level. This phenomenon, usually referred to as "space invaders scenario", is also known to occur for another $\textrm{AdS}_4$ solution based on a different squashed $S^7$., Comment: 35 pages, 6 figures, 12 tables, typos fixed, additional clarifications added. To appear on JHEP

We construct the M-Theory lifts of type IIA orientifolds based on K3-fibred Calabi-Yau threefolds with compatible involutions. Such orientifolds are shown to lift to M-Theory on twisted connected sum $G_2$ manifolds. Beautifully, the two building blocks forming the $G_2$ manifold correspond to the open and closed string sectors. As an application, we show how to use such lifts to explicitly study open string moduli. Finally, we use our analysis to construct examples of $G_2$ manifolds with different inequivalent TCS realizations., 41 pages, 3 figures; textual improvements and clarifications. To appear in JHEP

We show that the $D=11$ Supermembrane theory (M2-brane) compactified on a $M_9 \times T^2$ target space, with constant fluxes $C_{\pm}$ naturally incorporates the geometrical structure of a twisted torus. We extend the M2-brane theory to a formulation on a twisted torus bundle. It is consistently fibered over the world volume of the M2-brane. It can also be interpreted as a torus bundle with a nontrivial $U(1)$ connection associated to the fluxes. The structure group $G$ is the area preserving diffeomorphisms. The torus bundle is defined in terms of the monodromy associated to the isotopy classes of symplectomorphisms with $\pi_{0} (G) = SL(2,Z)$, and classified by the coinvariants of the subgroups of $SL(2,Z)$. The spectrum of the theory is purely discrete since the constant flux induces a central charge on the supersymmetric algebra and a modification on the Hamiltonian which renders the spectrum discrete with finite multiplicity. The theory is invariant under symplectomorphisms connected and non connected to the identity, a result relevant to guaranteed the U-dual invariance of the theory. The Hamiltonian of the theory exhibits interesting new $U(1)$ gauge and global symmetries on the worldvolume induced by the symplectomorphim transformations. We construct explicitly the supersymmetric algebra with nontrivial central charges. We show that the zero modes decouple from the nonzero ones. The nonzero mode algebra corresponds to a massive superalgebra that preserves either $1/2$ or $1/4$ of the original supersymmetry depending on the state considered., Comment: Latex, 27pg

We explore geometries that give rise to a novel algebraic structure, the Exceptional Drinfeld Algebra, which has recently been proposed as an approach to study generalised U-dualities, similar to the non-Abelian and Poisson-Lie generalisations of T-duality. This algebra is generically not a Lie algebra but a Leibniz algebra, and can be realised in exceptional generalised geometry or exceptional field theory through a set of frame fields giving a generalised parallelisation. We provide examples including "three-algebra geometries", which encode the structure constants for three-algebras and in some cases give novel uplifts for $CSO(p,q,r)$ gaugings of seven-dimensional maximal supergravity. We also discuss the M-theoretic embedding of both non-Abelian and Poisson-Lie T-duality., 24 pages + appendices + refs. v2: published version

Assuming Fiorenza-Sati-Schreiber's Hypothesis H, on the charge quantization of M-theory's $C$-field, the topological sectors of the resulting $String^{c_2}(4)$-valued higher gauge theory on a heterotic M5-brane are classified by homotopy classes of maps from the worldvolume $\Sigma_{M5}$ to $BString^{c_2}(4)$. This note calculates the sectors in a number of examples of M5-brane topology, including examples considered in the 3d-3d correspondence, the emergence of skyrmions from higher-dimensional instantons and Witten's analysis of the S-duality of 4d Yang-Mills theory., Comment: 16 pages; accepted version, some additional discussion

We study $\textrm{AdS}_2\times S^4 \times S^2 \times \Sigma_2$ solutions in type IIB string theory arising from D1 -- D3 -- NS5 brane intersections. These backgrounds enjoy sixteen supercharges and the corresponding internal geometry is non-compact due to the specific form of the warping w.r.t. the Riemann surface $\Sigma_2$. Even though a direct computation of the holographic free energy of the would-be dual CFT$_1$ yields a divergent behaviour, it reveals the typical $N^3$ scaling of a 6d theory upon introducing a hard cut-off. We claim that such geometries may be interpreted as the gravity duals of M(atrix) models describing an IR phase of the $(2,0)$ theory of M5 branes, in presence of momentum and NUT charges. We discuss parallel $\textrm{AdS}_2$ geometries describing longitudinal M2 branes in the UV, where the counting of the number of degrees of freedom correctly reproduces the expected $N^{3/2}$ behaviour of the dual field theory. These geometries provide explicit examples where deconstructed extra dimensions yield well-defined UV descriptions in terms of higher-dimensional CFTs., Comment: 32 pages, 1 appendix. v2: acknowledgements added

Supersymmetry allows a $D^4 R^4$ interaction in M-theory, but such an interaction is inconsistent with string theory dualities and so is known to be absent. We provide a novel proof of the absence of the $D^4 R^4$ M-theory interaction by calculating 4-point scattering amplitudes of 11d supergravitons from ABJM theory. This calculation extends a previous calculation performed to the order corresponding to the $R^4$ interaction. The new ingredient in this extension is the interpretation of the fourth derivative of the mass deformed $S^3$ partition function of ABJM theory, which can be determined using supersymmetric localization, as a constraint on the Mellin amplitude associated with the stress tensor multiplet 4-point function. As part of this computation, we relate the 4-point function of the superconformal primary of the stress tensor multiplet of any 3d ${\cal N} = 8$ SCFT to some of the 4-point functions of its superconformal descendants. We also provide a concise formula for a general integrated 4-point function on $S^d$ for any $d$., Comment: 54 pages, Mathematica notebook attached; v2 typos fixed

Tensor hierarchy algebras constitute a class of non-contragredient Lie superalgebras, whose finite-dimensional members are the "Cartan-type" Lie superalgebras in Kac's classification. They have applications in mathematical physics, especially in extended geometry and gauged supergravity. We further develop the recently proposed definition of tensor hierarchy algebras in terms of generators and relations encoded in a Dynkin diagram (which coincides with the diagram for a related Borcherds superalgebra). We apply it to cases where a grey node is added to the Dynkin diagram of a rank $r+1$ Kac-Moody algebra $\mathfrak{g}^+$, which in turn is an extension of a rank $r$ finite-dimensional semisimple simply laced Lie algebra $\mathfrak{g}$. The algebras are specified by $\mathfrak{g}$ together with a dominant integral weight $\lambda$. As a by-product, a remarkable identity involving representation matrices for arbitrary integral highest weight representations of $\mathfrak{g}$ is proven. An accompanying paper describes the application of tensor hierarchy algebras to the gauge structure and dynamics in models of extended geometry., Comment: 45 pp

We analyze the single subleading soft graviton theorem in $(d+1)$ dimensions under compactification on $S^1$. This produces the single soft theorems for the graviton, vector and scalar fields in $d$ dimension. For the compactification of $11$-dimensional supergravity theory, this gives the soft factorization properties of the single graviton, dilaton and RR 1-form fields in type IIA string theory in ten dimensions. For the case of the soft vector field, we also explicitly check the result obtained from compactification by computing the amplitudes with external massive spin two and massless finite energy states interacting with soft vector field. The former are the Kaluza-Klein excitations of the $d+1$ dimensional metric. Describing the interaction of the KK-modes with the vector field at each level by the minimally coupled Fierz-Pauli Lagrangian, we find agreement with the results obtained from the compactification if the gyromagnetic ratio in the minimally coupled Fierz-Pauli Lagrangian is taken to be $g=1$., Comment: 22 pages + appendix

In the quest for the mathematical formulation of M-theory, we consider three major open problems: a first-principles construction of the single (abelian) M5-brane Lagrangian density, the origin of the gauge field in heterotic M-theory, and the supersymmetric enhancement of exceptional M-geometry. By combining techniques from homotopy theory and from supergeometry to what we call super-exceptional geometry within super-homotopy theory, we present an elegant joint solution to all three problems. This leads to a unified description of the Nambu-Goto, Perry-Schwarz, and topological Yang-Mills Lagrangians in the topologically nontrivial setting. After explaining how charge quantization of the C-field in Cohomotopy reveals D'Auria-Fre's "hidden supergroup" of 11d supergravity as the super-exceptional target space, in the sense of Bandos, for M5-brane sigma-models, we prove, in exceptional generalization of the doubly-supersymmetric super-embedding formalism, that a Perry-Schwarz-type Lagrangian for single (abelian) M5-branes emerges as the super-exceptional trivialization of the M5-brane cocycle along the super-exceptional embedding of the "half" M5-brane locus, super-exceptionally compactified on the Horava-Witten circle fiber. From inspection of the resulting 5d super Yang-Mills Lagrangian we find that the extra fermion field appearing in super-exceptional M-geometry, whose physical interpretation had remained open, is the M-theoretic avatar of the gaugino field., Comment: 46 pages, v2: some comments and references added

We establish a higher generalization of super L-infinity-algebraic T-duality of super WZW-terms for super p-branes. In particular, we demonstrate spherical T-duality of super M5-branes propagating on exceptional-geometric 11d super spacetime., 51 pages, 2 figures, v2 has some typos fixed

We study the stress tensor multiplet four-point function in the 3d maximally supersymmetric ABJ(M) theory with Chern-Simons level $k=2$, which in the large $N$ limit is holographically dual to weakly coupled M-theory on $AdS_4\times S^7/\mathbb{Z}_2$. We use the Lorentzian inversion to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity $R$ and the first higher derivative correction $R^4$ vertices, up to a finite number of contact terms that contribute to low spins where the inversion formula does not converge. We find a precise match with the corresponding terms in the 11d M-theory S-matrix by taking the flat space limit, which is not sensitive to these contact terms. We then conjecturally fix these contact terms by analytically continuing the inversion formula below its expected range of convergence, and verify this conjecture using supersymmetric localization. Finally, we compare some of the 1-loop CFT data to non-perturbative in $N$ bounds from the numerical conformal bootstrap, which we compute at unprecedently high accuracy, and find that the 1-loop corrections saturate the bounds in the large $N$ regime, which extends the previously observed match at tree level., 47 pages + appendices, 3 figures. v3 typos corrected, accepted to JHEP

In this paper we derive Ward-Takahashi identities from the path integral of supersymmetric five-dimensional field theories with an $SU(1,3)$ spacetime symmetry in the presence of instantons. We explicitly show how $SU(1,3)$ is enhanced to $SU(1,3)\times U(1)$ where the additional $U(1)$ acts non-perturbatively. Solutions to such Ward-Takahashi identities were previously obtained from correlators of six-dimensional Lorentzian conformal field theories but where the instanton number was replaced by the momentum along a null direction. Here we study the reverse procedure whereby we construct correlation functions out of towers of five-dimensional operators which satisfy the Ward-Takahashi identities of a six-dimensional conformal field theory. This paves the way to computing observables in six dimensions using five-dimensional path integral techniques. We also argue that, once the instanton sector is included into the path integral, the coupling of the five-dimensional Lagrangian must be quantised, leaving no free continuous parameters., 40 pages. Technical details added in Section 3, and notation adjusted. Matches JHEP published version

We determine the mathematical structures which govern the Ω deformation of supersymmetric intersections of M2 and M5 branes. We find that the supersymmetric intersections govern many aspects of the theory of W-algebras, including degenerate modules, the Miura transform and Coulomb gas constructions. We give an algebraic interpretation of the Pandharipande-Thomas box counting in ℂ3.

The current classification of $\mathcal{N} = 1$ string theories in eight and seven dimensions is completely captured by K3 surfaces with F-Theory or M-Theory frozen singularities. In this note we show that there are inequivalent ways of freezing certain collections of singularities which have the same ADE type, and so there are more connected components in the moduli space than previously thought; namely, one more in eight dimensions and three more in seven dimensions. We argue that the new component in eight dimensions decompactifies to a string theory in nine dimensions with rank 1 gauge group, which has been so far unidentified. Constructing and studying the stringy descriptions corresponding to these moduli spaces is the subject of a companion paper., Comment: 15 pages + references, 1 figure

Warm dark matter particles with masses in the keV range have been linked with the large group representations in gauge theories through a high number of species at decoupling. In this paper, we address WDM fermionic degrees of freedom from such representations. Bridging higher-dimensional particle physics theories with cosmology studies and astrophysical observations, our approach is two-folded, i.e., it includes realistic models from higher-dimensional representations and constraints from simulations tested against observations. Starting with superalgebras in exceptional periodicity theories, we discuss several symmetry reductions and we consider several representations that accommodate a high number of degrees of freedom. We isolate a model that naturally accommodates both the standard model representation and the fermionic dark matter in agreement with both large and small-scale constraints. This model considers an intersection of branes in $D=27+3$ in a manner that provides the degrees of freedom for the standard model on one hand and 2048 fermionic degrees of freedom for dark matter, corresponding to a $\sim$2 keV particle mass, on the other. In this context, we discuss the theoretical implications and the observable predictions., Comment: Published in MDPI Universe as part of the Special Issue keV Warm Dark Matter ({\Lambda}WDM) in Agreement with Observations in Tribute to H\'ector J. De Vega

We derive major parts of the eigenvalue spectrum of the operators on the squashed seven-sphere that appear in the compactification of eleven-dimensional supergravity. These spectra determine the mass spectrum of the fields in $AdS_4$ and are important for the corresponding ${\mathcal N} =1$ supermultiplet structure. This work is a continuation of the work in [1] where the complete spectrum of irreducible isometry representations of the fields in $AdS_4$ was derived for this compactification. Some comments are also made concerning the $G_2$ holonomy and its implications on the structure of the operator equations on the squashed seven-sphere., Comment: 28 pages, v2: typos corrected, a footnote added

We derive a map relating the gauge symmetry groups of heterotic strings on $T^4$ to other components of the moduli space with rank reduction. This generalizes the results for $T^2$ and $T^3$ which mirror the singularity freezing mechanism of K3 surfaces in F and M-theory, respectively. The novel feature in six dimensions is that the map explicitly involves the topology of the gauge groups, in particular acting only on non-simply-connected ones. This relation is equivalent to that of connected components of the moduli space of flat $G$-bundles over $T^2$ with $G$ non-simply-connected. These results are verified with a reasonably exhaustive list of gauge groups obtained with a moduli space exploration algorithm., 27 pages, v2: minor corrections

In this work we study F-theory on symmetric toroidal orbifolds that exhibit roto-translations, which are point group rotations accompanied by fractional lattice shifts. These geometries admit a rich class of effects, such as twisted affine folded fibers, multiple fibers, and up to three distinct torus-fibrations that yield different M/F-theory lifts. We discuss the six-dimensional physics of the F-theory lifts, which generically host superconformal subsectors and a IIB axio-dilaton fixed to strong coupling. In addition we find that these theories exhibit a rich set of p=0,1,2 discrete p-form gauge symmetries. We discuss six-dimensional gauge and supergravity anomalies and match the rank and tensor branch dimension to the Hodge numbers that were computed using heterotic world sheet techniques., 39 pages plus appendix, 15 Figures, 2 Tables, V2 typos corrected

In the early universe it is important to take into account quantum effect of the gravity to explain the feature of the inflation. In this paper, we consider the M-theory effective action which consists of 11 dimensional supergravity and (Weyl)$^4$ terms. The equations of motion are solved perturbatively, and the solution describes the inflation-like expansion in 4 dimensional spacetime. Scalar and tensor perturbations around this background are evaluated analytically and their behaviors are investigated numerically. If we assume that these perturbations are constant at the beginning of the inflation, spectral indices for scalar and tensor perturbations become almost scale invariant., Comment: 21 pages, 5 figures, a reference added

The bosonic large-$N$ master field of the IIB matrix model can, in principle, give rise to an emergent classical spacetime. The task is then to calculate this master field as a solution of the bosonic master-field equation. We consider a simplified version of the algebraic bosonic master-field equation and take dimensionality $D=2$ and matrix size $N=6$. For an explicit realization of the pseudorandom constants entering this simplified algebraic equation, we establish the existence of a solution and find, after diagonalization of one of the two obtained matrices, a band-diagonal structure of the other matrix., 20 pages, v6: published version

We highlight what seems to be a remaining subtlety in the argument for the cancellation of the total anomaly associated with the M5-brane in M-theory. Then we prove that this subtlety is resolved under the hypothesis that the C-field flux is charge-quantized in the generalized cohomology theory called J-twisted Cohomotopy., Comment: 20 pages; v1: this is a revised version of Sections 2.5 and 4.5 in v1 of arXiv:1904.10207, which do not appear in the final version there; v2: main section 3 considerably expanded, analogous argument in Sec. 4.1 of arXiv:1910.04166 pointed out, appendix with supplementary proofs added

The involutory subalgebra K(E$_9$) of the affine Kac-Moody algebra E$_9$ was recently shown to admit an infinite sequence of unfaithful representations of ever increasing dimensions arXiv:2102.00870. We revisit these representations and describe their associated ideals in more detail, with particular emphasis on two chiral versions that can be constructed for each such representation. For every such unfaithful representation we show that the action of K(E$_9$) decomposes into a direct sum of two mutually commuting (`chiral' and `anti-chiral') parabolic algebras with Levi subalgebra $\mathfrak{so}(16)_+\,\oplus\,\mathfrak{so}(16)_-$. We also spell out the consistency conditions for uplifting such representations to unfaithful representations of K(E$_{10}$). From these results it is evident that the holonomy groups so far discussed in the literature are mere shadows (in a Platonic sense) of a much larger structure., 22 pages. v2: minor modifications and updated references; JHEP version