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In this paper, we show that the dynamics encoded in the nonlinear realization of the semi-direct product of the very extended algebra K 2 7 with its vector representation contains the low-energy effective action of the closed bosonic string. [ABSTRACT FROM AUTHOR]

In this paper, we study the relation of the M2-brane with fluxes and monodromy in SL(2, ℤ), which has a quantum discrete supersymmetric spectrum with finite multiplicity and type IIB gauged supergravities in nine dimensions. SL(2, ℤ) is the group of isotopy classes of the area-preserving diffeomorphisms. The global description of these M2-branes we are considering is formulated on twisted torus bundles, and they are classified in terms of H2(Σ, ℤρ), or equivalently, by their coinvariants for a given monodromy subgroup. We find the ‘gauge’ symmetries between equivalent M2-branes on torus bundles with monodromy that lead to ℝ, SO(2), or SO(1, 1), the symmetry groups of type IIB gauged supergravities in 9d. We obtain an explicit relation between the equivalent classes of M2-brane bundles and the mass parameters that classify the gaugings of type IIB supergravities in 9d. We also find that the symmetries between inequivalent M2-branes on twisted torus bundles for a given monodromy are related to ℤ, ℤ3, ℤ5, ℤ9, or ℤ2n − 7 for n ≥ 5, the U-duality symmetry group, a subgroup of SL(2, ℤ). In distinction, in the case without monodromy, related to type II maximal supergravity at low energies, its U-duality group corresponds to the full SL(2, ℤ). [ABSTRACT FROM AUTHOR]

We study half-BPS flows in gauged minimal 7d supergravity featured by an AdS3× S3 slicing of the metric, supported by a dyonic three-form field. We first present a novel strategy for analytic integration of the BPS equations, which makes use of the integrals of motion. Subsequently, we discuss the suitable choice of integration constants that gives rise to smooth geometries. These flows are asymptotically locally AdS7 and close off smoothly reproducing an AdS3× ℝ4 geometry. We then discuss their uplifts to 11d and massive IIA supergravity and observe that they describe one-parameter deformations of their AdS7× S4 and AdS7× S3 vacua, respectively, their holographic interpretation being as conformal defect CFT2’s within the corresponding dual SCFT6’s. We conclude with the computation of the holographic central charge, by focussing on the M-theory interpretation. [ABSTRACT FROM AUTHOR]

We explore the properties of Ω-deformed M-theory, with particular focus on the ℂ ϵ 1 × ℂ ϵ 2 × ℂ ϵ 3 background and coupling to Ω-deformed M2 and M5 brane world-volume theories. [ABSTRACT FROM AUTHOR]

We examine the giant graviton expansions of the Coulomb and Higgs indices for the M2-brane SCFTs to find the closed-form expressions for the indices that encode the spectra of the 1/4-BPS M5-brane giant gravitons and the 1/3-BPS orbifold M5-brane giant gravitons. Consequently, we get exact forms of the twisted indices for the 6d (2, 0) theories describing a stack of N M5-branes which generalize the unrefined indices. We confirm that they are also beautifully expanded with respect to the indices for the M2-brane giant gravitons which are obtained from the Coulomb and Higgs indices for the M2-brane SCFTs upon the change of variables. [ABSTRACT FROM AUTHOR]

In this work, we study the local zeta functions of Calabi-Yau fourfolds. This is done by developing arithmetic deformation techniques to compute the factor of the zeta function that is attributed to the horizontal four-form cohomology. This, in turn, is sensitive to the complex structure of the fourfold. Focusing mainly on examples of fourfolds with a single complex structure parameter, it is demonstrated that the proposed arithmetic techniques are both applicable and consistent. We present a Calabi-Yau fourfold for which a factor of the horizontal four-form cohomology further splits into two pieces of Hodge type (4, 0) + (2, 2) + (0, 4) and (3, 1) + (1, 3). The latter factor corresponds to a weight-3 modular form, which allows expressing the value of the periods in terms of critical values of the L-function of this modular form, in accordance with Deligne’s conjecture. The arithmetic considerations are related to M-theory Calabi-Yau fourfold compactifications with background four-form fluxes. We classify such background fluxes according to their Hodge type. For those fluxes associated to modular forms, we express their couplings in the low-energy effective action in terms of L-function values. [ABSTRACT FROM AUTHOR]

We study a non-relativistic limit of 11-dimensional supergravity. This limit leads to a theory with an underlying membrane Newton-Cartan geometry. Consistency of the non-relativistic limit requires the imposition of constraints, requiring that certain bosonic and fermionic torsions and curvatures vanish. We investigate the implications of two versions of these constraints. In one version, we keep only 16 supersymmetry transformations, leading to a simple (purely bosonic) constraint structure but an unusual realisation of the supersymmetry algebra which does not close into diffeomorphisms. In the other, we keep all 32 supersymmetry transformations. This requires a complicated sequence of bosonic and fermionic constraints, eventually involving three derivatives of bosonic fields. We argue, with a linearised calculation, that this sequence of constraints terminates. Furthermore, we show that there exists a family of supersymmetric solutions satisfying these constraints, containing the non-relativistic limit of the M2 supergravity solution recently obtained by Lambert and Smith as a background relevant for non-relativistic holography. [ABSTRACT FROM AUTHOR]

It was recently shown that integrating out M2 states on Calabi‐Yau manifolds captures non‐perturbative topological string physics in the free energy. In this note, It has been shown that the resulting expression manifests a certain duality symmetry: the free energy at strong string coupling is equal to the Calabi‐Yau period at weak string coupling. The duality yields the appropriate prescription for completing the integrating out in the ultraviolet. [ABSTRACT FROM AUTHOR]

We study half-BPS flows in gauged minimal 7d supergravity featured by an AdS3× S3 slicing of the metric, supported by a dyonic three-form field. We first present a novel strategy for analytic integration of the BPS equations, which makes use of the integrals of motion. Subsequently, we discuss the suitable choice of integration constants that gives rise to smooth geometries. These flows are asymptotically locally AdS7 and close off smoothly reproducing an AdS3× ℝ4 geometry. We then discuss their uplifts to 11d and massive IIA supergravity and observe that they describe one-parameter deformations of their AdS7× S4 and AdS7× S3 vacua, respectively, their holographic interpretation being as conformal defect CFT2’s within the corresponding dual SCFT6’s. We conclude with the computation of the holographic central charge, by focussing on the M-theory interpretation. [ABSTRACT FROM AUTHOR]

Abstract Construction of the superfield action of the N = (1, 0), d = 6 non-Abelian tensor multiplet based on the non-Abelian tensor hierarchies is considered. It is shown that while straightforward non-Abelian generalization of the Pasti-Sorokin-Tonin action is not a workable solution, a suitable truncation of the PST action still can be modified to include non-Abelian tensor field. In the modified action, the self-dual equation of motion of the tensor field is induced by a composite Lagrange multiplier, which is not a component of a standard dynamical tensor multiplet. As a result, the constraint that enforces the gauge group to be non-compact, as in the usual tensor hierarchies, can be avoided.

Abstract We study the global forms of class S A N − 1 $$ \mathcal{S}\left[{A}_{N-1}\right] $$ 4d N $$ \mathcal{N} $$ = 2 theories by deriving their defect groups (charges of line operators up to screening by local operators) from Coulomb branch data. Specifically, we employ an explicit construction of the BPS quiver for the case of full regular punctures to show that the defect group is (ℤ N )2g , where g is the genus of the associated Riemann surface. This determines a sector of surface operators in the 5d symmetry TFT. We show how these can also be identified from dimensional reduction of M-theory. We discuss connections to the theory of cluster algebras.

Abstract Drinfel’d doubles of Lie bialgebroids play an important role in T-duality of string theories. In the presence of H and R fluxes, Lie bialgebroids should be extended to proto Lie bialgebroids. For both cases, the pair is given by two dual vector bundles, and the Drinfel’d double yields a Courant algebroid. However for U-duality, more complicated direct sum decompositions that are not described by dual vector bundles appear. In a previous work, we extended the notion of a Lie bialgebroid for vector bundles that are not necessarily dual. We achieved this by introducing a framework of calculus on algebroids and examining compatibility conditions for various algebroid properties in this framework. Here our aim is two-fold: extending our work on bialgebroids to include both H- and R-twists, and generalizing proto Lie bialgebroids to pairs of arbitrary vector bundles. To this end, we analyze various algebroid axioms and derive twisted compatibility conditions in the presence of twists. We introduce the notion of proto bialgebroids and their Drinfel’d doubles, where the former generalizes both bialgebroids and proto Lie bialgebroids. We also examine the most general form of vector bundle automorphisms of the double, related to twist matrices, that generate a new bracket from a given one. We analyze various examples from both physics and mathematics literatures in our framework.

Abstract We consider two supersymmetric M5 brane probe solutions in AdS7 × S 4 and one in AdS4 × S 7 that all have the AdS3 × S 3 world-volume geometry. The values of the classical action of the first two M5 probes (with S 3 in AdS7 or in S 4) are related to the leading N 2 parts in the anomaly b-coefficient in the (2,0) theory corresponding to a spherical surface defect in symmetric or antisymmetric SU(N) representations. We present a detailed computation of the corresponding one-loop M5 brane partition functions finding that they vanish (in a particular regularization). This implies the vanishing of the order N 0 part in the b-anomaly coefficients, in agreement with earlier predictions for their exact values. It remains, however, a puzzle of how to reproduce the non-vanishing order N terms in these coefficients within the semiclassical M5-brane probe setup.

Abstract We explore the symmetry structure of Type II Little String Theories and their T-dualities. We construct these theories both from the bottom-up perspective starting with seed Superconformal Field Theories, and from the top-down using F-/M-theory. By exploiting anomaly inflow and unitarity of the LST worldsheet theory, we derive strong conditions on the possible 6D bulk theories and their flavor algebras. These constraints continue to apply if gravity is coupled to the theory. We also study the higher form symmetry structure of these theories and show how they get exchanged under T-duality. Finally, we comment on seemingly consistent bottom-up Little String Theories that cannot be constructed from the top-down approach.

Abstract The quantization of semiclassical strings in AdS spacetimes yields predictions for the strong-coupling behaviour of the scaling dimensions of the corresponding operators in the planar limit of the dual gauge theory. Finding non-planar corrections requires computing string loops (corresponding to torus and higher genus surfaces), which is a challenging task. It turns out that in the case of the U k (N) × U −k (N) ABJM theory there is an alternative approach: one may semiclassically quantize M2 branes in AdS4 × S 7 /ℤ k which are wrapped around the 11d circle of radius 1/k = λ/N . Such M2 branes are the M-theory generalization of the strings in AdS × CP3. In this work, we show that by expanding in large M2 brane tension T 2 ~ kN $$ \sqrt{kN} $$ for fixed k, followed by an expansion in large k, we can predict the large λ asymptotics of the non-planar corrections to the dimensions of the dual ABJM operators. As a specific example, we consider the M2 brane configuration that generalizes the long folded string with large spin in AdS4, and compute the 1-loop correction to its energy. This calculation allows us to determine non-planar corrections to the universal scaling function or cusp anomalous dimension. We extend our analysis to the semiclassical M2 branes that generalize the “short” and “long” circular strings with two equal angular momenta in CP3. The “short” M2 brane corresponds to a dual operator whose dimension at strong coupling scales as ∆ ∼ λ 1/4 + …, and we derive the leading non-planar correction to it.

Abstract Recently we have constructed a completely supersymmetric nonlinear action possessing the properties expected from multiple D0-brane system. Its quantization should result in an interesting supersymmetric field theory in the (super)space with additional matrix coordinates which can provide an important insights in the study of String Theory. As a first stage toward this aim, in this paper we construct the Hamiltonian mechanics and perform covariant quantization of the simplest three dimensional counterpart of the ten dimensional multiple D0-brane model. We obtain a supersymmetric system of equations in a (super)spacetime enlarged by bosonic and fermionic matrix coordinates which appears as a result of such quantization and discuss some of its properties.

Abstract We analyse the backreacted geometry corresponding to a stack of M5-branes wrapped on a spindle, with a view towards precision tests of the dual N $$ \mathcal{N} $$ = 1 superconformal field theory. We carefully study the singular loci of the uplifted geometry and show that these correspond to C 3/Z n conical singularities. Therefore, these solutions present one of the first explicit realisations of honest locally N $$ \mathcal{N} $$ = 1 preserving punctures in class S $$ \mathcal{S} $$ . Additionally we study the symmetries and anomalies of the dual field theory through anomaly inflow and compute a variety of holographic observables including dimensions of BPS operators. This work paves the way for advancements in the study and identification of the precise dual field theories.

Abstract We propose precise effective field theory criteria to obtain a four-dimensional de Sitter space within M-theory. To this effect, starting with the state space described by the action of metric perturbations, fluxes etc over the supersymmetric Minkowski vacuum in eleven-dimensions, we discuss the most general low energy effective action in terms of the eleven-dimensional fields including non-perturbative and non-local terms. Given this, our criteria to obtain a valid four-dimensional de Sitter solution at far IR involve satisfying the Schwinger-Dyson equations of the associated path integral, as well as obeying positivity constraints on the dual IIA string coupling and its time derivative. For excited states, the Schwinger-Dyson equations imply an effective emergent potential different from the original potential. We show that while vacuum solutions and arbitrary coherent states fail to satisfy these criteria, a specific class of excited states called the Glauber-Sudarshan states obey them. Using the resurgent structure of observables computed using the path integral over the Glauber-Sudarshan states, four-dimensional de Sitter in the flat slicing can be constructed using a Glauber-Sudarshan state in M-theory. Among other novel results, we discuss the smallness of the positive cosmological constant, including the curious case where the cosmological constant is very slowly varying with time. We also discuss the resolution of identity with the Glauber-Sudarshan states, generation and the convergence properties of the non-perturbative and the non-local effects, the problems with the static patch and other related topics. We analyze briefly the issues related to the compatibility of the Wilsonian effective action with Borel resummations and discuss how they influence the effective field theory description in a four-dimensional de Sitter space.

Abstract We study the superconformal index of 3d N $$ \mathcal{N} $$ = 2 superconformal field theories on S 1 × ω S 2 in the Cardy-like limit where the radius of the S 1 is much smaller than that of the S 2. We show that the first two leading terms in this Cardy-like expansion are dictated by the Bethe Ansatz formulation of the topologically twisted index of the same theory. We apply this relation to 3d N $$ \mathcal{N} $$ = 2 holographic superconformal field theories describing the low-energy dynamics of N M2-branes and derive closed form expressions, valid to all orders in the 1/N expansion, for the two leading terms in the Cardy-like expansion of the superconformal index. We also discuss the implications of our results for the entropy of supersymmetric Kerr-Newman black holes in AdS4 and the four-derivative corrections to 4d gauged supergravity.

Abstract We show that integrating out M2 branes ending on M5 branes inside Calabi-Yau manifolds captures non-perturbative open topological string physics. The integrating out is performed using a contour integral in complexified Schwinger proper time. For the resolved conifold, this contour can be extended to include the zero pole, which we argue captures the ultraviolet completion of the integrating out and yields the tree-level polynomial terms in the free energy. This is a manifestation of the Emergence Proposal, and provides further evidence for it. Unlike the case of closed strings, where the emergent terms are kinetic terms in the action, for these open strings it is tree-level potential terms which are emergent. This provides a first quantitative example of the proposal that classical tree-level potentials in string theory emerge from integrating out co-dimension one states.

Abstract One of the pertinent question in the analysis of de Sitter as an excited state is what happens to the Glauber-Sudarshan states that are off-shell, i.e. the states that do not satisfy the Schwinger-Dyson equations. We argue that these Glauber-Sudarshan states, including the on-shell ones, are controlled by a bigger envelope wave functional namely a wave functional of the universe which surprisingly satisfies a Wheeler-De Witt equation. We provide various justification of the aforementioned identification including the determination of the emergent Hamiltonian constraint appearing in the Wheeler-De Witt equation that is satisfied by both the on- and off-shell states. Our analysis provides further evidence of why a transient four-dimensional de Sitter phase in string theory should be viewed as an excited state over a supersymmetric warped Minkowski background and not as a vacuum state.

Abstract Given a manifold M $$ \mathbbm{M} $$ admitting a maximally supersymmetric consistent truncation, we show how to formulate new consistent truncations by restricting to a set of Kaluza-Klein modes on M $$ \mathbbm{M} $$ invariant under some subgroup of the group of isometries of M $$ \mathbbm{M} $$ . These truncations may involve either finite or infinite sets of modes. We provide their global description using exceptional generalised geometry to construct a ‘deformed’ generalised parallelisation starting with that on M $$ \mathbbm{M} $$ . This allows us to explicitly embed known consistent truncations directly into exceptional generalised geometry/exceptional field theory, and to obtain the equations governing situations where the consistent truncation retains an infinite tower of modes.

Abstract We use the duality between gravitational dynamics and fluids living on dynamical surfaces carrying multiple charges, known as the blackfold approach, to perturbatively construct new asymptotically global (Anti)-de Sitter multi-spinning, non-extremal, multi-charged black holes in theories of higher-dimensional gravity minimally coupled to a dilaton and higher-form gauge fields in spacetime dimensions D ≥ 5, and new asymptotically AdS l × S m black holes in type IIB and eleven-dimensional supergravity. These solutions include the generalisation of the Kerr-Newman solution to (A)dS carrying either electric or string charge, generalisations of black rings to higher-dimensions with 𝕊 p × 𝕊 n+1 horizon topology, static de Sitter solutions carrying arbitrary q-brane charge, as well as various asymptotically AdS l × S m multi-charged and multi-spinning black hole solutions, some of which correspond to novel thermal states in N $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory.

Our goal in this paper is to give a brief survey of recent developments in the study of M-theory on singular Calabi–Yau three-folds, topological strings in the presence of a flat but topologically nontrivial B-field and their relationship to hybrid phases of certain Gauged Linear Sigma Models (GLSM). [ABSTRACT FROM AUTHOR]

Recent no‐go theorems have ruled out four‐dimensional classical de Sitter vacua in heterotic string theory. On the other hand, the absence of a well‐defined Wilsonian effective action and other related phenomena also appear to rule out such time‐dependent vacua with de Sitter isometries, even in the presence of quantum corrections. In this note, the authors argued that a four‐dimensional de Sitter space can still exist in SO(32)$SO(32)$ heterotic string theory as a Glauber–Sudarshan state, i.e., as an excited state, over a supersymmetric Minkowski background, albeit within a finite temporal domain. Borel resummation and resurgence play a crucial role in constructing such a state in the Hilbert space of heterotic theory governed entirely by the IR degrees of freedom. [ABSTRACT FROM AUTHOR]

We explore the symmetry structure of Type II Little String Theories and their T-dualities. We construct these theories both from the bottom-up perspective starting with seed Superconformal Field Theories, and from the top-down using F-/M-theory. By exploiting anomaly inflow and unitarity of the LST worldsheet theory, we derive strong conditions on the possible 6D bulk theories and their flavor algebras. These constraints continue to apply if gravity is coupled to the theory. We also study the higher form symmetry structure of these theories and show how they get exchanged under T-duality. Finally, we comment on seemingly consistent bottom-up Little String Theories that cannot be constructed from the top-down approach. [ABSTRACT FROM AUTHOR]

The quantization of semiclassical strings in AdS spacetimes yields predictions for the strong-coupling behaviour of the scaling dimensions of the corresponding operators in the planar limit of the dual gauge theory. Finding non-planar corrections requires computing string loops (corresponding to torus and higher genus surfaces), which is a challenging task. It turns out that in the case of the Uk(N) × U−k(N) ABJM theory there is an alternative approach: one may semiclassically quantize M2 branes in AdS4 × S7/ℤk which are wrapped around the 11d circle of radius 1/k = λ/N. Such M2 branes are the M-theory generalization of the strings in AdS × CP3. In this work, we show that by expanding in large M2 brane tension T2 ~ kN for fixed k, followed by an expansion in large k, we can predict the large λ asymptotics of the non-planar corrections to the dimensions of the dual ABJM operators. As a specific example, we consider the M2 brane configuration that generalizes the long folded string with large spin in AdS4, and compute the 1-loop correction to its energy. This calculation allows us to determine non-planar corrections to the universal scaling function or cusp anomalous dimension. We extend our analysis to the semiclassical M2 branes that generalize the “short” and “long” circular strings with two equal angular momenta in CP3. The “short” M2 brane corresponds to a dual operator whose dimension at strong coupling scales as ∆ ∼ λ1/4 + …, and we derive the leading non-planar correction to it. [ABSTRACT FROM AUTHOR]

We show that integrating out M2 branes ending on M5 branes inside Calabi-Yau manifolds captures non-perturbative open topological string physics. The integrating out is performed using a contour integral in complexified Schwinger proper time. For the resolved conifold, this contour can be extended to include the zero pole, which we argue captures the ultraviolet completion of the integrating out and yields the tree-level polynomial terms in the free energy. This is a manifestation of the Emergence Proposal, and provides further evidence for it. Unlike the case of closed strings, where the emergent terms are kinetic terms in the action, for these open strings it is tree-level potential terms which are emergent. This provides a first quantitative example of the proposal that classical tree-level potentials in string theory emerge from integrating out co-dimension one states. [ABSTRACT FROM AUTHOR]

One of the pertinent question in the analysis of de Sitter as an excited state is what happens to the Glauber-Sudarshan states that are off-shell, i.e. the states that do not satisfy the Schwinger-Dyson equations. We argue that these Glauber-Sudarshan states, including the on-shell ones, are controlled by a bigger envelope wave functional namely a wave functional of the universe which surprisingly satisfies a Wheeler-De Witt equation. We provide various justification of the aforementioned identification including the determination of the emergent Hamiltonian constraint appearing in the Wheeler-De Witt equation that is satisfied by both the on- and off-shell states. Our analysis provides further evidence of why a transient four-dimensional de Sitter phase in string theory should be viewed as an excited state over a supersymmetric warped Minkowski background and not as a vacuum state. [ABSTRACT FROM AUTHOR]

We study the superconformal index of 3d N = 2 superconformal field theories on S1 ×ωS2 in the Cardy-like limit where the radius of the S1 is much smaller than that of the S2. We show that the first two leading terms in this Cardy-like expansion are dictated by the Bethe Ansatz formulation of the topologically twisted index of the same theory. We apply this relation to 3d N = 2 holographic superconformal field theories describing the low-energy dynamics of N M2-branes and derive closed form expressions, valid to all orders in the 1/N expansion, for the two leading terms in the Cardy-like expansion of the superconformal index. We also discuss the implications of our results for the entropy of supersymmetric Kerr-Newman black holes in AdS4 and the four-derivative corrections to 4d gauged supergravity. [ABSTRACT FROM AUTHOR]

We propose precise effective field theory criteria to obtain a four-dimensional de Sitter space within M-theory. To this effect, starting with the state space described by the action of metric perturbations, fluxes etc over the supersymmetric Minkowski vacuum in eleven-dimensions, we discuss the most general low energy effective action in terms of the eleven-dimensional fields including non-perturbative and non-local terms. Given this, our criteria to obtain a valid four-dimensional de Sitter solution at far IR involve satisfying the Schwinger-Dyson equations of the associated path integral, as well as obeying positivity constraints on the dual IIA string coupling and its time derivative. For excited states, the Schwinger-Dyson equations imply an effective emergent potential different from the original potential. We show that while vacuum solutions and arbitrary coherent states fail to satisfy these criteria, a specific class of excited states called the Glauber-Sudarshan states obey them. Using the resurgent structure of observables computed using the path integral over the Glauber-Sudarshan states, four-dimensional de Sitter in the flat slicing can be constructed using a Glauber-Sudarshan state in M-theory. Among other novel results, we discuss the smallness of the positive cosmological constant, including the curious case where the cosmological constant is very slowly varying with time. We also discuss the resolution of identity with the Glauber-Sudarshan states, generation and the convergence properties of the non-perturbative and the non-local effects, the problems with the static patch and other related topics. We analyze briefly the issues related to the compatibility of the Wilsonian effective action with Borel resummations and discuss how they influence the effective field theory description in a four-dimensional de Sitter space. [ABSTRACT FROM AUTHOR]

We analyse the backreacted geometry corresponding to a stack of M5-branes wrapped on a spindle, with a view towards precision tests of the dual N = 1 superconformal field theory. We carefully study the singular loci of the uplifted geometry and show that these correspond to C3/Zn conical singularities. Therefore, these solutions present one of the first explicit realisations of honest locally N = 1 preserving punctures in class S . Additionally we study the symmetries and anomalies of the dual field theory through anomaly inflow and compute a variety of holographic observables including dimensions of BPS operators. This work paves the way for advancements in the study and identification of the precise dual field theories. [ABSTRACT FROM AUTHOR]

Recently we have constructed a completely supersymmetric nonlinear action possessing the properties expected from multiple D0-brane system. Its quantization should result in an interesting supersymmetric field theory in the (super)space with additional matrix coordinates which can provide an important insights in the study of String Theory. As a first stage toward this aim, in this paper we construct the Hamiltonian mechanics and perform covariant quantization of the simplest three dimensional counterpart of the ten dimensional multiple D0-brane model. We obtain a supersymmetric system of equations in a (super)spacetime enlarged by bosonic and fermionic matrix coordinates which appears as a result of such quantization and discuss some of its properties. [ABSTRACT FROM AUTHOR]

Given a manifold M admitting a maximally supersymmetric consistent truncation, we show how to formulate new consistent truncations by restricting to a set of Kaluza-Klein modes on M invariant under some subgroup of the group of isometries of M . These truncations may involve either finite or infinite sets of modes. We provide their global description using exceptional generalised geometry to construct a ‘deformed’ generalised parallelisation starting with that on M . This allows us to explicitly embed known consistent truncations directly into exceptional generalised geometry/exceptional field theory, and to obtain the equations governing situations where the consistent truncation retains an infinite tower of modes. [ABSTRACT FROM AUTHOR]

We use the duality between gravitational dynamics and fluids living on dynamical surfaces carrying multiple charges, known as the blackfold approach, to perturbatively construct new asymptotically global (Anti)-de Sitter multi-spinning, non-extremal, multi-charged black holes in theories of higher-dimensional gravity minimally coupled to a dilaton and higher-form gauge fields in spacetime dimensions D ≥ 5, and new asymptotically AdSl × Sm black holes in type IIB and eleven-dimensional supergravity. These solutions include the generalisation of the Kerr-Newman solution to (A)dS carrying either electric or string charge, generalisations of black rings to higher-dimensions with 핊p × 핊n+1 horizon topology, static de Sitter solutions carrying arbitrary q-brane charge, as well as various asymptotically AdSl× Sm multi-charged and multi-spinning black hole solutions, some of which correspond to novel thermal states in N = 4 Super-Yang-Mills theory. [ABSTRACT FROM AUTHOR]

Abstract We show that the (1,0) tensor and hypermultiplet supersymmetry variations can be uplifted to loop space. Upon dimensional reduction we make contact with abelian five-dimensional super Yang-Mills, which has a nonabelian generalization that we subsequently uplift back to loop space where we conjecture a nonabelian generalization of the (1,0) supersymmetry variations and demonstrate their on-shell closure.

Abstract We explore the T-duality web of 6D Heterotic Little String Theories, focusing on flavor algebra reducing deformations. A careful analysis of the full flavor algebra, including Abelian factors, shows that the flavor rank is preserved under T-duality. This suggests a new T-duality invariant in addition to the Coulomb branch dimension and the two-group structure constants. We also engineer Little String Theories with non-simply laced flavor algebras, whose appearance we attribute to certain discrete 3-form fluxes in M-theory. Geometrically, these theories are engineered in F-theory with non-Kähler favorable K3 fibers. This geometric origin leads us to propose that freezing fluxes are preserved across T-duality. Along the way, we discuss various exotic models, including two inequivalent Spin(32)/ℤ2 models that are dual to the same E8 × E8 theory, and a family of self-T-dual models.

Abstract Higher-group symmetries are combinations of higher-form symmetries which appear in various field theories. In this paper, we explain how higher-group symmetries arise in 10d and 11d supergravities when the latter are coupled to brane sources. Motivated by this observation, we study field theories at zero and finite temperature invariant under a class of continuous Abelian higher-group symmetries. We restrict the analysis to the low-energy regime where the dynamical field content exclusively consists of Goldstone fields arising from the spontaneous breaking of higher-group and spacetime symmetries. Invariant quantities are constructed and the phases of matter are classified according to the pattern of spontaneous symmetry breaking. With respect to supergravity, we highlight how such Goldstone effective theories provide a symmetry-based interpretation for the theories living on D/M-branes. As an explicit example we construct a 6-group invariant action for the bosonic M5 brane, consistent with the self-duality of the 3-form field strength on the brane. While the self-duality condition in the bosonic case needs to be imposed externally as a constraint at zero temperature, we find an equilibrium effective action for the bosonic M5 brane at finite temperature that inherently implements self-duality.

Abstract We construct the teleparallel dynamics for extended geometry where the structure algebra is (an extension of) an untwisted affine Kac-Moody algebra. This provides a geometrisation of the Geroch symmetry appearing on dimensional reduction of a gravitational theory to two dimensions. The formalism is adapted to the underlying tensor hierarchy algebra, and will serve as a stepping stone towards the geometrisation of other infinite-dimensional, e.g. hyperbolic, symmetries.

Abstract We compute the one-loop 2 → 2 scattering amplitude of massless scalars on the world volume of an infinite D = 11 supermembrane quantized in the static gauge. The resulting expression is manifestly finite and turns out to be much simpler than in the bosonic membrane case in arXiv:2308.12189 being proportional to the tree-level scattering amplitude. We also consider the case of ℝ 1, 1 × S 1 membrane with one dimension compactified on a circle of radius R and demonstrate how the supermembrane scattering amplitude reduces to the one on an infinite D = 10 Green-Schwarz superstring in the limit of R→ 0.

Abstract Flux quantization of the C-field in 11d supergravity is arguably necessary for the (UV-)completion of the theory, in that it determines the torsion charges carried by small numbers N ≪ ∞ of M-branes. However, hypotheses about C-field flux-quantization (“models of the C-field”) have previously been discussed only in the bosonic sector of 11d supergravity and ignoring the supergravity equations of motion. Here we highlight a duality-symmetric formulation of on-shell 11d supergravity on superspace, observe that this naturally lends itself to completion of the theory by flux quantization, and indeed that 11d super-spacetimes are put on-shell by carrying quantizable duality-symmetric super-C-field flux; the proof of which we present in detail.

Abstract We extend the notion of Lie bialgebroids for more general bracket structures used in string and M theories. We formalize the notions of calculus and dual calculi on algebroids. We achieve this by reinterpreting the main results of the matched pairs of Leibniz algebroids. By examining a rather general set of fundamental algebroid axioms, we present the compatibility conditions between two calculi on vector bundles which are not dual in the usual sense. Given two algebroids equipped with calculi satisfying the compatibility conditions, we construct its double on their direct sum. This generalizes the Drinfel’d double of Lie bialgebroids. We discuss several examples from the literature including exceptional Courant brackets. Using Nambu-Poisson structures, we construct an explicit example, which is important both from physical and mathematical point of views. This example can be considered as the extension of triangular Lie bialgebroids in the realm of higher Courant algebroids, that automatically satisfy the compatibility conditions. We extend the Poisson generalized geometry by defining Nambu-Poisson exceptional generalized geometry and prove some preliminary results in this framework. We also comment on the global picture in the framework of formal rackoids and we slightly extend the notion for vector bundle valued metrics.

Abstract We study the duality between the ABJ(M) theory at Chern-Simons level k = 4 and the orientifold ABJ theory at Chern-Simons level k = 1 by using the S 3 partition function. The partition function can be computed using the supersymmetric localization in terms of a matrix model, and we derive an ideal Fermi gas system by applying the Fermi gas formalism to the matrix model. By using this formalism, we show that the matrix model can be embedded in the partition function of A ̂ $$ \hat{A} $$ 3 or D ̂ $$ \hat{D} $$ 3 quiver theories, and the equality of these quiver theories, which comes from A ̂ $$ \hat{A} $$ 3 = D ̂ $$ \hat{D} $$ 3, leads to exact relations of the matrix models. These exact relations can be used to check the identification of the flavor symmetries. The perfect agreement between the matrix models also implies that no decoupled sector is needed.

Abstract Geometric engineering is a collection of tools developed to establish dictionaries between local singularities in string theory and (supersymmetric) quantum fields. Extended operators and defects, as well as their higher quantum numbers captured by topological symmetries, can be encoded within geometric engineering dictionaries. In this paper we revisit and clarify aspects of these techniques, with special emphasis on ’t Hooft anomalies, interpreted from the SymTFT perspective as obstructions to the existence of Neumann boundary conditions. These obstructions to gauging higher symmetries are captured via higher link correlators for the SymTFT on spheres. In this work, we give the geometric engineering counterpart of this construction in terms of higher links of topological membranes. We provide a consistency check in the context of 5D SCFTs with anomalous 1-form symmetries, where we give two independent derivations of the anomaly in terms of higher links, one purely field theoretical and the other purely geometrical. Along the way, we also recover the construction of non-invertible duality defects in 4D N $$ \mathcal{N} $$ = 4 SYM from a geometric engineering perspective.

Abstract We construct the Fermi gas formalism for the partition function of supersymmetric Chern-Simons theories with affine D-type quiver diagrams with non-uniform ranks of the gauge groups and Fayet-Illiopoulos parameters by two different approaches: the open string formalism and the closed string formalism. In the closed string formalism approach, we find a novel connection between the partition function of this theory and the partition function of a four-nodes circular quiver supersymmetric Chern-Simons theory. We also studied a symmetry of a density matrix appeared in the closed string formalism. We further calculate the exact values of the partition function for finite N, with which we identified the exponent of the leading non-perturbative effect in 1/N corresponding to the worldsheet instantons in the circular quiver supersymmetric Chern-Simons theories.

Abstract The Emergence Proposal suggests that some Swampland criteria, in particular on large field distances, are a consequence of the emergent nature of dynamics for fields in the infrared. In the context of type II string theory compactified on Calabi-Yau manifolds, it proposes that the cubic tree-level piece of the genus-zero prepotential is emergent from integrating out massive non-perturbative states. For a certain special non-compact Calabi-Yau, the blown-up conifold, it is known that the full all-genus prepotential can be matched onto the Grand Canonical potential of a two-dimensional Fermi gas. We propose here that this should be understood in the context of emergence: the prepotential is induced by integrating out the Fermi gas degrees of freedom. To make contact with the Swampland we need dynamical gravity, so compact Calabi-Yau manifolds. We show that for specifically the cubic term, an integrating out calculation also works for compact cases. In particular, the exact cubic term coefficient can be recovered from integrating out a Fermi gas for any compact Calabi-Yau that is an elliptic fibration over a reflexive toric base. We also propose a general map, for any one-parameter Calabi-Yau, between the Grand Canonical potential of the ultraviolet non-perturbative system and the period. In particular, this map leads to an emergent cubic term in the genus-zero prepotential for any such one-parameter model.

Abstract It has been recently suggested that the strong Emergence Proposal is realized in M-theory limits by integrating out all light towers of states with a typical mass scale not larger than the species scale, i.e. the eleventh dimensional Planck mass. Within the BPS sector, these are transverse M2- and M5-branes, that can be wrapped and particle-like, carrying Kaluza-Klein momentum along the compact directions. We provide additional evidence for this picture by revisiting and investigating further the computation of R 4-interactions in M-theory à la Green-Gutperle-Vanhove. A central aspect is a novel UV-regularization of Schwinger-like integrals, whose actual meaning and power we clarify by first applying it to string perturbation theory. We consider then toroidal compactifications of M-theory and provide evidence that integrating out all light towers of states via Schwinger-like integrals thus regularized yields the complete result for R 4-interactions. In particular, this includes terms that are tree-level, one-loop and space-time instanton corrections from the weakly coupled point of view. Finally, we comment on the conceptual difference of our approach to earlier closely related work by Kiritsis-Pioline and Obers-Pioline, leading to a correspondence between two types of constrained Eisenstein series.

Abstract We study the bosonic sector of a decoupling limit of type IIA superstring theory, where a background Ramond-Ramond one-form is fined tuned to its critical value, such that it cancels the associated background D0-brane tension. The light excitations in this critical limit are D0-branes, whose dynamics is described by the Banks-Fischler-Shenker-Susskind (BFSS) Matrix theory that corresponds to M-theory in the Discrete Light-Cone Quantization (DLCQ). We develop the worldsheet formalism for the fundamental string in the same critical limit of type IIA superstring theory. We show that the fundamental string develops singularities on its worldsheet, whose topology is described by nodal Riemann spheres as in ambitwistor string theory. We study the T-duality transformations of this string sigma model and provide a worldsheet derivation for the recently revived and expanded duality web that unifies a zoo of decoupling limits in type II superstring theories. By matching the string worldsheet actions, we demonstrate how some of these decoupling limits are related to tensionless (and ambitwistor) string theory, Carrollian string theory, the Spin Matrix limits of the AdS/CFT correspondence, and more.

Abstract We study M-Theory solutions with G-flux on the Fermat sextic Calabi-Yau fourfold, focussing on the relationship between the number of stabilized complex structure moduli and the tadpole contribution of the flux. We use two alternative approaches to define the fluxes: algebraic cycles and (appropriately quantized) Griffiths residues. In both cases, we collect evidence for the non-existence of solutions which stabilize all moduli and stay within the tadpole bound.