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Abstract We consider 3d N $$ \mathcal{N} $$ = 2 non-abelian Hanany-Witten brane setups with chiral flavor symmetry. We propose that the associated field theories are quivers with improved bifundamentals, instead of standard bifundamentals. The improved bifundamental is a strongly coupled SCFT that carries one more U(1) global symmetry than the standard bifundamental. As a consequence, our proposal overcomes the long standing challenge of associating to each N $$ \mathcal{N} $$ = 2 brane setup a gauge theory with the full rank global symmetry, allowing the study of all the usual supersymmetric observables, such as superconformal index, sphere partition function, chiral ring and moduli space. The construction passes many non-trivial tests, for instance we algorithmically prove that any two improved quivers associated to S $$ \mathcal{S} $$ -dual brane setups are infrared dual. The 3d N $$ \mathcal{N} $$ = 2 mirror dualities can be uplifted to 4d dualities with 4d improved bifundamentals connecting USp(2N) nodes.

Abstract A new type of quiver theories, denoted twin quivers, was recently introduced for studying 5d SCFTs engineered by webs of 5-branes ending on 7-branes. Twin quivers provide an alternative perspective on various aspects of such webs, including Hanany-Witten moves and the s-rule. More ambitiously, they can be regarded as a first step towards the construction of combinatorial objects, generalizing brane tilings, encoding the corresponding BPS quivers. This paper continues the investigation of twin quivers, focusing on their non-uniqueness, which stems from the multiplicity of toric phases for a given toric Calabi-Yau 3-fold. We find that the different twin quivers are necessary for describing what we call quiver tails, which in turn correspond to certain sub-configurations in the webs. More generally, the multiplicity of twin quivers captures the roots of the Higgs branch in the extended Coulomb branch of 5d theories.

Abstract The Coulomb and Higgs indices of the 3d N $$ \mathcal{N} $$ = 4 U(N) ADHM theories can be decorated by line defect operators as the line defect correlators. We obtain exact closed-form expressions and various non-trivial algebraic relations for the correlators of the Wilson lines in the fundamental and (anti)symmetric representations by means of the Hall-Littlewood expansion, the Fermi-gas method and the residue calculation. From the large N limit of the correlators we obtain the single particle gravity indices which are expected to encode the spectra of fluctuation modes on the gravity duals of line operators in M2-brane SCFTs.

Abstract We consider 5d KK dualities, that is multiple 5d gauge theories with the same 6d infinite coupling limit. We provide a prescription to associate 4d N $$ \mathcal{N} $$ = 1 quivers to the 5d dual quivers, such that the 4d quivers are also dual to each other. The 4d dualities are infrared dualities which can be checked matching global symmetry anomalies and in certain cases can be proven using basic Seiberg dualities sequentially. We also consider dualities obtained by Higgsing in two different ways the same 5d theory, in some simple examples.

Abstract We propose and test a novel conjectural relation satisfied by the superconformal index of maximally supersymmetric U(N) gauge theory in four dimensions. Analogous relations appear to be also valid for the superconformal indices of a large collection of other gauge theories, as well as for a broad class of index-like generating functions. The relation expresses the finite N index as a systematic series of corrections to a large N answer. Individual corrections have an holographic interpretation as the analytic continuation of contributions from “giant graviton” branes fixed by a specific symmetry generator.

Abstract We revisit the problem of defining an invariant notion of tension in gravity. For spacetimes whose asymptotics are those of a Defect CFT we propose two independent definitions: gravitational tension given by the one-point function of the dilatation current, and inertial tension, or stiffness, given by the norm of the displacement operator. We show that both reduce to the tension of the Nambu-Goto action in the limit of classical thin-brane probes. Subtle normalisations of the relevant Witten diagrams are fixed by the Weyl and diffeomorphism Ward identities of the boundary DCFT. The gravitational tension is not defined for domain walls, whereas stiffness is not defined for point particles. When they both exist these two tensions are in general different, but the examples of line and surface BPS defects in d = 4 show that superconformal invariance can identify them.

Abstract We consider a 1 2 $$ \frac{1}{2} $$ -BPS solution for a D3 brane probe in AdS5 × S 5 that has world-volume geometry of AdS3 × S 1. It intersects the boundary over a surface that represents a dimension 2 defect in the boundary N $$ \mathcal{N} $$ = 4 SYM theory. The effective action of the probe brane is proportional to the logarithmically divergent volume of AdS3 and may thus be interpreted as computing conformal anomaly of supersymmetric S 2 defect. The classical action scales as N. We compute the 1-loop correction to it due to quantum fluctuations of the D3 brane world-volume fields and compare the result to an earlier suggested expression for the defect anomaly. We also perform a similar analysis of a 1 2 $$ \frac{1}{2} $$ -BPS M5 brane probe solution in AdS7 × S 4 with the world-volume geometry of AdS5 × S 1 that represents a dimension 4 defect in the boundary (2,0) 6d theory. Here the classical M5 brane action computes the leading order N 2 term in a-anomaly of the supersymmetric S 4 defect. We perform a detailed computation of the 1-loop correction to the M5 brane effective action and thus provide a prediction for the subleading constant in the S 4 defect a-anomaly coefficient.

Abstract We study, from the perspective of supersymmetry and space-time Killing spinors, the local brane densities involved in 1/4-BPS intersecting brane systems. In particular, we classify the possible local brane structures that have maximal (16) supersymmetries in 1/4-BPS intersecting brane backgrounds. Applied to BPS black holes, this classification reveals the allowed local microstructure for pure microstates. We further use these structures with local 16 supersymmetries as building blocks to generalise to 1/8-BPS systems. Moreover, we give examples of 1/8-BPS black holes for which the local supersymmetries are compatible with the combination of different entropy-generating effects from brane interaction. Finally, applying our classification to BPS domain walls, we illustrate how our formalism may possibly describe the local picture of the Hanany-Witten effect.

Abstract We study marginal deformations of N $$ \mathcal{N} $$ = 2, d = 4 long linear quiver CFTs using the holographic description. We find a two-parameter family of AdS5 solutions that generically break all of supersymmetry, but preserve N $$ \mathcal{N} $$ = 1 for a particular tuning of the parameters. We study the G-structure of the N $$ \mathcal{N} $$ = 2 “parent” and the N $$ \mathcal{N} $$ = 1 backgrounds and carefully discuss the quantisation of charges in all cases. For the N $$ \mathcal{N} $$ = 1 and N $$ \mathcal{N} $$ = 0 cases, a picture emerges with “branes” back-reacted on either a spindle or its higher dimensional analogue. Comments on the marginally deformed dual CFTs are given, together with the study of some observables.

Abstract In this paper, we study massless/massive vector and p-form field perturbations in AdS spacetime with an end-of-the-world brane. By imposing Υ(1) preserving Neumann boundary condition on the end-of-the-world brane, we study their spectrum and discuss their implications for dual BCFT operators. When the perturbation is massless, the dual BCFT operator is a conserved current and we show that such an operator indeed satisfies the Υ(1) preserving conformal boundary condition. On the other hand, when the perturbation is massive, in general there exists non-vanishing perpendicular components of the dual BCFT operator, even in the massless limit. We explain this difference between massless and massive perturbations from the point of view of the bulk gauge symmetry, or equivalently from different structure of equations of motion. We also find several brane-tension-independent modes in massless perturbations, and these are understood as boundary-condition-independent modes from the dual BCFT point of view.

We revisit the problem of defining an invariant notion of tension in gravity. For spacetimes whose asymptotics are those of a Defect CFT we propose two independent definitions: gravitational tension given by the one-point function of the dilatation current, and inertial tension, or stiffness, given by the norm of the displacement operator. We show that both reduce to the tension of the Nambu-Goto action in the limit of classical thin-brane probes. Subtle normalisations of the relevant Witten diagrams are fixed by the Weyl and diffeomorphism Ward identities of the boundary DCFT. The gravitational tension is not defined for domain walls, whereas stiffness is not defined for point particles. When they both exist these two tensions are in general different, but the examples of line and surface BPS defects in d = 4 show that superconformal invariance can identify them. [ABSTRACT FROM AUTHOR]

We study marginal deformations of N = 2, d = 4 long linear quiver CFTs using the holographic description. We find a two-parameter family of AdS5 solutions that generically break all of supersymmetry, but preserve N = 1 for a particular tuning of the parameters. We study the G-structure of the N = 2 “parent” and the N = 1 backgrounds and carefully discuss the quantisation of charges in all cases. For the N = 1 and N = 0 cases, a picture emerges with “branes” back-reacted on either a spindle or its higher dimensional analogue. Comments on the marginally deformed dual CFTs are given, together with the study of some observables. [ABSTRACT FROM AUTHOR]

We consider a 1 2 -BPS solution for a D3 brane probe in AdS5× S5 that has world-volume geometry of AdS3× S1. It intersects the boundary over a surface that represents a dimension 2 defect in the boundary N = 4 SYM theory. The effective action of the probe brane is proportional to the logarithmically divergent volume of AdS3 and may thus be interpreted as computing conformal anomaly of supersymmetric S2 defect. The classical action scales as N. We compute the 1-loop correction to it due to quantum fluctuations of the D3 brane world-volume fields and compare the result to an earlier suggested expression for the defect anomaly. We also perform a similar analysis of a 1 2 -BPS M5 brane probe solution in AdS7× S4 with the world-volume geometry of AdS5× S1 that represents a dimension 4 defect in the boundary (2,0) 6d theory. Here the classical M5 brane action computes the leading order N2 term in a-anomaly of the supersymmetric S4 defect. We perform a detailed computation of the 1-loop correction to the M5 brane effective action and thus provide a prediction for the subleading constant in the S4 defect a-anomaly coefficient. [ABSTRACT FROM AUTHOR]

We study, from the perspective of supersymmetry and space-time Killing spinors, the local brane densities involved in 1/4-BPS intersecting brane systems. In particular, we classify the possible local brane structures that have maximal (16) supersymmetries in 1/4-BPS intersecting brane backgrounds. Applied to BPS black holes, this classification reveals the allowed local microstructure for pure microstates. We further use these structures with local 16 supersymmetries as building blocks to generalise to 1/8-BPS systems. Moreover, we give examples of 1/8-BPS black holes for which the local supersymmetries are compatible with the combination of different entropy-generating effects from brane interaction. Finally, applying our classification to BPS domain walls, we illustrate how our formalism may possibly describe the local picture of the Hanany-Witten effect. [ABSTRACT FROM AUTHOR]

In this paper, we study massless/massive vector and p-form field perturbations in AdS spacetime with an end-of-the-world brane. By imposing Υ(1) preserving Neumann boundary condition on the end-of-the-world brane, we study their spectrum and discuss their implications for dual BCFT operators. When the perturbation is massless, the dual BCFT operator is a conserved current and we show that such an operator indeed satisfies the Υ(1) preserving conformal boundary condition. On the other hand, when the perturbation is massive, in general there exists non-vanishing perpendicular components of the dual BCFT operator, even in the massless limit. We explain this difference between massless and massive perturbations from the point of view of the bulk gauge symmetry, or equivalently from different structure of equations of motion. We also find several brane-tension-independent modes in massless perturbations, and these are understood as boundary-condition-independent modes from the dual BCFT point of view. [ABSTRACT FROM AUTHOR]

Abstract We report a novel BPS jumping phenomenon of 5d N $$ \mathcal{N} $$ = 1 supersymmetric gauge theories whose brane configuration is equipped with an O7-plane. The study of the relation between O7+-plane and O7 − -plane reveals that such BPS jumps take place when the Higgsing is triggered near the O7-plane upon a particular parameter tuning of the theories. We propose two types of gauge theories whose BPS spectra jump. One is the SU(2N + 8) gauge theory with a symmetric hypermultiplet converted to the SU(2N) gauge theory with an antisymmetric hypermultiplet. The other is pure SO(2N + 8) gauge theory jumping to pure Sp(N) gauge theory. We explicitly confirm our proposal through the (un)refined instanton partition functions. Furthermore, we discuss feasible generalizations involving an Op-plane for supersymmetric gauge theories of eight supercharges in four and three dimensions (p = 6, 5 respectively).

Abstract This paper introduces two operations in quiver gauge theories. The first operation, collapse, takes a quiver with a permutation symmetry S n and gives a quiver with adjoint loops. The corresponding 3d N $$ \mathcal{N} $$ = 4 Coulomb branches are related by an orbifold of S n . The second operation, multi-lacing, takes a quiver with n nodes connected by edges of multiplicity k and replaces them by n nodes of multiplicity qk. The corresponding Coulomb branch moduli spaces are related by an orbifold of type ℤ q n − 1 $$ {\mathbb{Z}}_q^{n-1} $$ . Collapse generalises known cases that appeared in the literature [1–3]. These two operations can be combined to generate new relations between moduli spaces that are constructed using the magnetic construction.

Abstract We study 3D N $$ \mathcal{N} $$ = 2 supersymmetric field theories geometrically engineered from M-theory on non-compact Calabi-Yau fourfolds (CY4). We establish a detailed dictionary between the geometry and topology of non-compact CY4 and the physics of 3D N $$ \mathcal{N} $$ = 2 theories in three different regimes. The first one is the Coulomb branch description when the CY4 is smooth. The second one is non-abelian gauge theory when the CY4 has a degenerate ℙ1-fibration structure. The third one is the strongly coupled SCFT from a CY4 singularity. We find interesting flavor symmetry enhancements in the singular limit of CY4, as well as an interesting and previously unexplored phenomenon in 3D, termed “flavor symmetry duality”. Many examples are analyzed with an emphasis on toric CY4s and ℂ4 orbifolds with crepant resolutions. We develop a new brane box method to study the physics of Coulomb branch of 3D N $$ \mathcal{N} $$ = 2 theory that admits a toric construction. Via IIB/M-theory duality we find that the brane box diagram living in ℝ3 can be physically realized as a configuration of intersecting 4-branes which are extended objects in 8D maximal supersymmetric theory, which is shown to be consistent via various chains of dualities. The rank, effective gauge coupling and certain hints to flavor symmetry enhancement of the 3D N $$ \mathcal{N} $$ = 2 theory are read off from the brane box and cross-checked against the results obtained from geometric engineering. The exotic branes in 8D maximal supersymmetric theory and the 4-string junctions thereof are shown to play a crucial role in the construction of the brane box.

Abstract We compute the spectra associated with various semiclassical string states that propagate over N $$ \mathcal{N} $$ = 2 Gaiotto-Maldacena backgrounds. As an interesting special case, for the Abelian T- dual solution, we discover giant magnon and single spike configurations while imposing appropriate boundary conditions. However, for Sfetsos-Thompson backgrounds, one has to adopt a different string embedding which reveals “modified” dispersion relations both for magnons and spikes. These results boil down into the standard dispersion relations in the limit when the rank of the associated SU(N c ) color gauge group becomes large enough. We further generalize our analysis in the presence of flavor D6 branes. Our analysis reveals a new set of dispersion relations, which shows that both magnons and spikes are ceased to exist in the presence of flavor excitations.

Abstract We generalize recent methods regarding the construction of complete prepotentials of five dimensional SCFTs to two classes of rank-N theories, i.e. the X 1,N and the UV fixed point of the SU (N + 1)0 + 2(N + 1)F gauge theories. Their complete prepotentials are consistently constructed starting from their weakly coupled descriptions. The results are verified by employing UV dualities and decoupling of flavors from theories with known complete prepotentials. Applications of these results to the recent investigation of non-supersymmetric conformal field theories from soft supersymmetric breaking deformations are addressed.

Abstract We compute the equivariant partition function of the six-dimensional M-string SCFTs on a background with the topology of a product of a two-dimensional torus and an ALE singularity. We determine the result by exploiting BPS strings probing the singularity, whose worldvolume theories we determine via a chain of string dualities. A distinguished feature we observe is that for this class of background the BPS strings’ worldsheet theories become relative field theories that are sensitive to finer discrete data generalizing to 6d the familiar choices of flat connections at infinity for instantons on ALE spaces. We test our proposal against a conjectural 6d N $$ \mathcal{N} $$ = (1, 0) generalization of the Nekrasov master formula, as well as against known results on ALE partition functions in four dimensions.

Abstract We study the counting problem of BPS D-branes wrapping holomorphic cycles of a general toric Calabi-Yau manifold. We evaluate the Jeffrey-Kirwan residues for the flavoured Witten index for the supersymmetric quiver quantum mechanics on the worldvolume of the D-branes, and find that BPS degeneracies are described by a statistical mechanical model of crystal melting. For Calabi-Yau threefolds, we reproduce the crystal melting models long known in the literature. For Calabi-Yau fourfolds, however, we find that the crystal does not contain the full information for the BPS degeneracy and we need to explicitly evaluate non-trivial weights assigned to the crystal configurations. Our discussions treat Calabi-Yau threefolds and fourfolds on equal footing, and include discussions on elliptic and rational generalizations of the BPS states counting, connections to the mathematical definition of generalized Donaldson-Thomas invariants, examples of wall crossings, and of trialities in quiver gauge theories.

Abstract We propose two novel methods for computing the superconformal index of 5d superconformal field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves the use of Higgs branch flows from UV Lagrangian theories, guided by transitions in 5-brane webs in Type IIB string theory. The second method employs the relationship between O7+-plane and O7 − -plane with eight D7-branes, which applies to particular non-Lagrangian theories realized by brane configurations involving an O7+-plane. As a concrete application of our method, we compute the superconformal indices for all known rank-1 non-Lagrangian theories, which we also use to identify flavor symmetries and their global forms at the conformal field theory (CFT) fixed points.

Abstract We introduce a class of 4-dimensional crystal melting models that count the BPS bound state of branes on toric Calabi-Yau 4-folds. The crystalline structure is determined by the brane brick model associated to the Calabi-Yau 4-fold under consideration or, equivalently, its dual periodic quiver. The crystals provide a discretized version of the underlying toric geometries. We introduce various techniques to visualize crystals and their melting configurations, including 3-dimensional slicing and Hasse diagrams. We illustrate the construction with the D0-D8 system on $${\mathbb{C}}$$ 4. Finally, we outline how our proposal generalizes to arbitrary toric CY 4-folds and general brane configurations.

We report a novel BPS jumping phenomenon of 5d N = 1 supersymmetric gauge theories whose brane configuration is equipped with an O7-plane. The study of the relation between O7+-plane and O7−-plane reveals that such BPS jumps take place when the Higgsing is triggered near the O7-plane upon a particular parameter tuning of the theories. We propose two types of gauge theories whose BPS spectra jump. One is the SU(2N + 8) gauge theory with a symmetric hypermultiplet converted to the SU(2N) gauge theory with an antisymmetric hypermultiplet. The other is pure SO(2N + 8) gauge theory jumping to pure Sp(N) gauge theory. We explicitly confirm our proposal through the (un)refined instanton partition functions. Furthermore, we discuss feasible generalizations involving an Op-plane for supersymmetric gauge theories of eight supercharges in four and three dimensions (p = 6, 5 respectively). [ABSTRACT FROM AUTHOR]

This paper introduces two operations in quiver gauge theories. The first operation, collapse, takes a quiver with a permutation symmetry Sn and gives a quiver with adjoint loops. The corresponding 3d N = 4 Coulomb branches are related by an orbifold of Sn. The second operation, multi-lacing, takes a quiver with n nodes connected by edges of multiplicity k and replaces them by n nodes of multiplicity qk. The corresponding Coulomb branch moduli spaces are related by an orbifold of type ℤ q n − 1 . Collapse generalises known cases that appeared in the literature [1–3]. These two operations can be combined to generate new relations between moduli spaces that are constructed using the magnetic construction. [ABSTRACT FROM AUTHOR]

We compute the spectra associated with various semiclassical string states that propagate over N = 2 Gaiotto-Maldacena backgrounds. As an interesting special case, for the Abelian T- dual solution, we discover giant magnon and single spike configurations while imposing appropriate boundary conditions. However, for Sfetsos-Thompson backgrounds, one has to adopt a different string embedding which reveals “modified” dispersion relations both for magnons and spikes. These results boil down into the standard dispersion relations in the limit when the rank of the associated SU(Nc) color gauge group becomes large enough. We further generalize our analysis in the presence of flavor D6 branes. Our analysis reveals a new set of dispersion relations, which shows that both magnons and spikes are ceased to exist in the presence of flavor excitations. [ABSTRACT FROM AUTHOR]

We study 3D N = 2 supersymmetric field theories geometrically engineered from M-theory on non-compact Calabi-Yau fourfolds (CY4). We establish a detailed dictionary between the geometry and topology of non-compact CY4 and the physics of 3D N = 2 theories in three different regimes. The first one is the Coulomb branch description when the CY4 is smooth. The second one is non-abelian gauge theory when the CY4 has a degenerate ℙ1-fibration structure. The third one is the strongly coupled SCFT from a CY4 singularity. We find interesting flavor symmetry enhancements in the singular limit of CY4, as well as an interesting and previously unexplored phenomenon in 3D, termed “flavor symmetry duality”. Many examples are analyzed with an emphasis on toric CY4s and ℂ4 orbifolds with crepant resolutions. We develop a new brane box method to study the physics of Coulomb branch of 3D N = 2 theory that admits a toric construction. Via IIB/M-theory duality we find that the brane box diagram living in ℝ3 can be physically realized as a configuration of intersecting 4-branes which are extended objects in 8D maximal supersymmetric theory, which is shown to be consistent via various chains of dualities. The rank, effective gauge coupling and certain hints to flavor symmetry enhancement of the 3D N = 2 theory are read off from the brane box and cross-checked against the results obtained from geometric engineering. The exotic branes in 8D maximal supersymmetric theory and the 4-string junctions thereof are shown to play a crucial role in the construction of the brane box. [ABSTRACT FROM AUTHOR]

We generalize recent methods regarding the construction of complete prepotentials of five dimensional SCFTs to two classes of rank-N theories, i.e. the X1,N and the UV fixed point of the SU (N + 1)0 + 2(N + 1)F gauge theories. Their complete prepotentials are consistently constructed starting from their weakly coupled descriptions. The results are verified by employing UV dualities and decoupling of flavors from theories with known complete prepotentials. Applications of these results to the recent investigation of non-supersymmetric conformal field theories from soft supersymmetric breaking deformations are addressed. [ABSTRACT FROM AUTHOR]

We compute the equivariant partition function of the six-dimensional M-string SCFTs on a background with the topology of a product of a two-dimensional torus and an ALE singularity. We determine the result by exploiting BPS strings probing the singularity, whose worldvolume theories we determine via a chain of string dualities. A distinguished feature we observe is that for this class of background the BPS strings' worldsheet theories become relative field theories that are sensitive to finer discrete data generalizing to 6d the familiar choices of flat connections at infinity for instantons on ALE spaces. We test our proposal against a conjectural 6d N = (1, 0) generalization of the Nekrasov master formula, as well as against known results on ALE partition functions in four dimensions. [ABSTRACT FROM AUTHOR]

We propose two novel methods for computing the superconformal index of 5d superconformal field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves the use of Higgs branch flows from UV Lagrangian theories, guided by transitions in 5-brane webs in Type IIB string theory. The second method employs the relationship between O7+-plane and O7−-plane with eight D7-branes, which applies to particular non-Lagrangian theories realized by brane configurations involving an O7+-plane. As a concrete application of our method, we compute the superconformal indices for all known rank-1 non-Lagrangian theories, which we also use to identify flavor symmetries and their global forms at the conformal field theory (CFT) fixed points. [ABSTRACT FROM AUTHOR]

We study the counting problem of BPS D-branes wrapping holomorphic cycles of a general toric Calabi-Yau manifold. We evaluate the Jeffrey-Kirwan residues for the flavoured Witten index for the supersymmetric quiver quantum mechanics on the worldvolume of the D-branes, and find that BPS degeneracies are described by a statistical mechanical model of crystal melting. For Calabi-Yau threefolds, we reproduce the crystal melting models long known in the literature. For Calabi-Yau fourfolds, however, we find that the crystal does not contain the full information for the BPS degeneracy and we need to explicitly evaluate non-trivial weights assigned to the crystal configurations. Our discussions treat Calabi-Yau threefolds and fourfolds on equal footing, and include discussions on elliptic and rational generalizations of the BPS states counting, connections to the mathematical definition of generalized Donaldson-Thomas invariants, examples of wall crossings, and of trialities in quiver gauge theories. [ABSTRACT FROM AUTHOR]

We introduce a class of 4-dimensional crystal melting models that count the BPS bound state of branes on toric Calabi-Yau 4-folds. The crystalline structure is determined by the brane brick model associated to the Calabi-Yau 4-fold under consideration or, equivalently, its dual periodic quiver. The crystals provide a discretized version of the underlying toric geometries. We introduce various techniques to visualize crystals and their melting configurations, including 3-dimensional slicing and Hasse diagrams. We illustrate the construction with the D0-D8 system on 4. Finally, we outline how our proposal generalizes to arbitrary toric CY 4-folds and general brane configurations. [ABSTRACT FROM AUTHOR]

Abstract We study to what extent, and in what form, the notion of gauge-string duality may persist at finite N. It is shown, in the half-BPS sector, that the states of D3 giant graviton branes in AdS5 × S 5 are holographically dual to certain auxiliary ghosts that compensate for finite N trace relations in U(N) N $$ \mathcal{N} $$ = 4 super Yang-Mills. The complex formed from spaces of states of bulk D3 giants is observed to furnish a BRST-like resolution of the half-BPS Hilbert space of U(N) N $$ \mathcal{N} $$ = 4 SYM at finite N. We argue that the identification between the states of certain bulk D-branes and the auxiliary ghosts in the boundary holds rather generally at vanishing ’t Hooft coupling λ = 0. We propose that a complex, which furnishes a BRST-like resolution of the finite N Hilbert space of a boundary U(N) gauge theory at λ = 0, should be identified as the space of states of the dual string theory in the α′ → ∞ limit. The Lefschetz trace formula provides the holographic map in this regime, where bulk observables are computed by taking the alternating sum of the expectation values in an ensemble of states built on each open string vacuum. The giant graviton expansion is recovered and generalized in a limit of the resolution.

Abstract We study the large N dynamics of two massless Yang-Mills coupled matrix quantum mechanics, by minimization of a loop truncated Jevicki-Sakita effective collective field Hamiltonian. The loop space constraints are handled by the use of master variables. The method is successfully applied directly in the massless limit for a range of values of the Yang-Mills coupling constant, and the scaling behaviour of different physical quantities derived from their dimensions are obtained with a high level of precision. We consider both planar properties of the theory, such as the large N ground state energy and multi-matrix correlator expectation values, and also the spectrum of the theory. For the spectrum, we establish that the U(N) traced fundamental constituents remain massless and decoupled from other states, and that bound states develop well defined mass gaps, with the mass of the two degenerate lowest lying bound states being determined with a particularly high degree of accuracy. In order to confirm, numerically, the physical interpretation of the spectrum properties of the U(N) traced constituents, we add masses to the system and show that, indeed, the U(N) traced fundamental constituents retain their “bare masses”. For this system, we draw comparisons with planar results available in the literature.

Abstract We begin a study of the Higgs branch of six-dimensional (1, 0) little string theories governing the worldvolumes of heterotic ALE instantons. We give a description of this space by constructing the corresponding magnetic quiver. The latter is a three-dimensional N $$ \mathcal{N} $$ = 4 quiver gauge theory that flows in the infrared to a fixed point whose quantum corrected Coulomb branches is the Higgs branch of the six-dimensional theory of interest. We present results for both types of heterotic strings, and mostly for ℂ2 /ℤ k ALE spaces. Our analysis is valid both in the absence and in the presence of small instantons. Along the way, we also describe small SO(32) instanton transitions in terms of the corresponding magnetic quiver, which parallels a similar treatment of the small E 8 instanton transitions in the context of the E 8 × E 8 heterotic string.

Abstract We study the Symmetry Topological Field Theory in holography associated with 4d 𝒩 = 1 Super Yang-Mills theory with gauge algebra 𝔰𝔲(M). From this, all the bulk symmetry operators are computed and matched to various D-brane configurations. The fusion algebra of the operators emerges from brane dynamics. In particular, we show that the symmetry operators are purely determined from the center-of-mass modes of the branes. We identify the TQFT fusion coefficients with the relative motion of the branes. We also establish the origin of condensation defects, arising from fusion of non-invertible operators, as the consequence of tachyon condensation in brane-anti-brane pairs.

Abstract The connection between two recent descriptions of tensor hierarchies — namely, infinity-enhanced Leibniz algebroids, given by Bonezzi & Hohm and Lavau & Palmkvist, and the p-brane QP-manifolds constructed by Arvanitakis — is made precise. This is done by presenting a duality-covariant version of latter. The construction is based on the QP-manifold T ⋆[n]T[1]M × ℋ[n], where M corresponds to the internal manifold of a supergravity compactification and ℋ[n] to a degree-shifted version of the infinity-enhanced Leibniz algebroid. Imposing that the canonical Q-structure on T ⋆[n]T[1]M is the derivative operator on ℋ leads to a set of constraints. Solutions to these constraints correspond to 1 2 $$ \frac{1}{2} $$ -BPS p-branes, suggesting that this is a new incarnation of a brane scan. Reduction w.r.t. to these constraints reproduces the known p-brane QP-manifolds. This is shown explicitly for the SL(3)×SL(2)- and SL(5)-theories. Furthermore, this setting is used to speculate about exceptional ‘extended spaces’ and QP-manifolds associated to Leibniz algebras. A proposal is made to realise differential graded manifolds associated to Leibniz algebras as non-Poisson subspaces (i.e. not Poisson reductions) of QP-manifolds similar to the above. Two examples for this proposal are discussed: generalised fluxes (including the dilaton flux) of O(d, d) and the 3-bracket flux for the SL(5)-theory.

We study to what extent, and in what form, the notion of gauge-string duality may persist at finite N. It is shown, in the half-BPS sector, that the states of D3 giant graviton branes in AdS5 × S5 are holographically dual to certain auxiliary ghosts that compensate for finite N trace relations in U(N) N = 4 super Yang-Mills. The complex formed from spaces of states of bulk D3 giants is observed to furnish a BRST-like resolution of the half-BPS Hilbert space of U(N) N = 4 SYM at finite N. We argue that the identification between the states of certain bulk D-branes and the auxiliary ghosts in the boundary holds rather generally at vanishing ’t Hooft coupling λ = 0. We propose that a complex, which furnishes a BRST-like resolution of the finite N Hilbert space of a boundary U(N) gauge theory at λ = 0, should be identified as the space of states of the dual string theory in the α′ → ∞ limit. The Lefschetz trace formula provides the holographic map in this regime, where bulk observables are computed by taking the alternating sum of the expectation values in an ensemble of states built on each open string vacuum. The giant graviton expansion is recovered and generalized in a limit of the resolution. [ABSTRACT FROM AUTHOR]

We study the large N dynamics of two massless Yang-Mills coupled matrix quantum mechanics, by minimization of a loop truncated Jevicki-Sakita effective collective field Hamiltonian. The loop space constraints are handled by the use of master variables. The method is successfully applied directly in the massless limit for a range of values of the Yang-Mills coupling constant, and the scaling behaviour of different physical quantities derived from their dimensions are obtained with a high level of precision. We consider both planar properties of the theory, such as the large N ground state energy and multi-matrix correlator expectation values, and also the spectrum of the theory. For the spectrum, we establish that the U(N) traced fundamental constituents remain massless and decoupled from other states, and that bound states develop well defined mass gaps, with the mass of the two degenerate lowest lying bound states being determined with a particularly high degree of accuracy. In order to confirm, numerically, the physical interpretation of the spectrum properties of the U(N) traced constituents, we add masses to the system and show that, indeed, the U(N) traced fundamental constituents retain their “bare masses”. For this system, we draw comparisons with planar results available in the literature. [ABSTRACT FROM AUTHOR]

We study the Symmetry Topological Field Theory in holography associated with 4d 풩 = 1 Super Yang-Mills theory with gauge algebra 픰픲(M). From this, all the bulk symmetry operators are computed and matched to various D-brane configurations. The fusion algebra of the operators emerges from brane dynamics. In particular, we show that the symmetry operators are purely determined from the center-of-mass modes of the branes. We identify the TQFT fusion coefficients with the relative motion of the branes. We also establish the origin of condensation defects, arising from fusion of non-invertible operators, as the consequence of tachyon condensation in brane-anti-brane pairs. [ABSTRACT FROM AUTHOR]

Abstract We construct Seiberg-Witten curves for 5d N $$ \mathcal{N} $$ = 1 gauge theories whose Type IIB 5-brane configuration involves an O7-plane and discuss an intriguing relation between theories with an O7+-plane and those with an O7 − -plane and 8 D7-branes. We claim that 5-brane configurations with an O7+-plane can be effectively understood as 5-brane configurations with a set of an O7 − -plane and eight D7-branes with some special tuning of their masses such that the D7-branes are frozen at the O7 − -plane. We check this equivalence between SU(N) gauge theory with a symmetric hypermultiplet and SU(N) gauge theory with an antisymmetric with 8 fundamentals, and also between SO(2N) gauge theory and Sp(N) gauge theory with eight fundamentals. We also compute the Seiberg-Witten curves for non-Lagrangian theories with a symmetric hypermultiplet, which includes the local ℙ2 theory with an adjoint.

Abstract We study systems with an Adler-Bell-Jackiw anomaly in terms of non-invertible symmetry. We present a new kind of non-invertible charge defect where a key role is played by a local current operator localized on the defect. The charge defects are now labeled by elements of a continuous (1). We use this construction to prove an analogue of Goldstone’s theorem for such non-invertible symmetries. We comment on possible applications to string theory.

Abstract We study particular families of bad 3d N $$ \mathcal{N} $$ = 4 quiver gauge theories, whose Higgs branches consist of many cones. We show the role of a novel brane configuration in realizing the Higgs moduli for each distinct cone. Through brane constructions, magnetic quivers, Hasse diagrams, and Hilbert series computations we study the intricate structure of the classical Higgs branches. These Higgs branches are both non-normal (since they consist of multiple cones) and non-reduced (due to the presence of nilpotent operators in the chiral ring). Applying the principle of inversion to the classical Higgs branch Hasse diagrams, we conjecture the quantum Coulomb branch Hasse diagrams. These Coulomb branches have several most singular loci, corresponding to the several cones in the Higgs branch. We propose the Hasse diagrams of the full quantum moduli spaces of our theories. The quivers we study can be taken to be 5d effective gauge theories living on brane webs. Their infinite coupling theories have Higgs branches which also consist of multiple cones. Some of these cones have decorated magnetic quivers, whose 3d Coulomb branches remain elusive.

Abstract We describe the higher-form and non-invertible symmetries of 4d N $$ \mathcal{N} $$ = 3 S-folds using the brane dynamics of their holographic duals. In cases with enhancement to N $$ \mathcal{N} $$ = 4 supersymmetry, our analysis reproduces the known field theory results of Aharony, Seiberg and Tachikawa, and is compatible with the effective action recently given by Bergman and Hirano. Likewise, for two specific N $$ \mathcal{N} $$ = 3 theories for which Zafrir has conjectured N $$ \mathcal{N} $$ = 1 Lagrangians our results agree with those implied by the Lagrangian description. In all other cases, our results imply novel predictions about the symmetries of the corresponding N $$ \mathcal{N} $$ = 3 field theories.

Abstract Recently, a large class of 3d 𝒩 = 2 gauge theories with mixed Chern-Simons levels, corresponding to plumbing 3-manifolds, has been identified. In this paper we generalize these theories by including in their content chiral multiples, and analyze their properties. We find that the content of such theories can be encoded in graphs, which generalize plumbing graphs, and various operations in these theories can be represented in terms of transformations of such graphs. The operations in question include gauging global symmetries, integrating out gauge nodes, which for theories without chiral multiplets corresponds to Kirby moves, and ST-transformations that involve chiral multiplets. The dualities such as mirror triality and SQED-XYZ duality can be also represented in terms of graphs, and enable us to find many new dual theories by gauging global symmetries. In particular, we find that gauged SQED-XYZ duality leads to other dualities, which take the same form as operations of linking and unlinking discussed in the context of knots-quivers correspondence. We also find that the superpotential can be encoded in an interesting class of triangle graphs that satisfy certain consistency conditions, we discuss decoupling and Higgsing of chiral multiplets, as well as interpretation of various phenomena in terms of brane webs.

Abstract The BFSS matrix model relates flat space M-theory to a large N limit of matrix quantum mechanics describing N non-relativistic D0-branes. M-theory, being a theory of gravity in flat space, has a rich infrared structure that includes various soft theorems and an infinite set of conserved charges associated to asymptotic symmetries. In this work, we ask: to what extent is this infrared structure present in BFSS? We find that all the salient features concerning the infrared structure of M-theory carry over naturally to the quantum mechanics dual. Moreover, we demonstrate that the dual statement of the soft graviton theorem in the matrix model implies that D0-brane scattering amplitudes in BFSS enjoy the full 11d Lorentz symmetry of M-theory, a claim which has been long anticipated. We also offer several first-principle consistency checks for our findings, including a computation of the soft theorem which does not presuppose the BFSS duality and a non-trivial match between several known symmetries of M-theory and BFSS that appear naturally in this formalism. These calculations give non-perturbative evidence in support of the BFSS duality as a model of flat space holography.