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Shadow formalism is a technique in two-dimensional CFT allowing straightforward computation of conformal blocks in the limit of infinitely large central charge. We generalize the construction of shadow operator for superconformal field theories. We demonstrate that shadow formalism yields known expressions for the large-c limit of the four-point superconformal block on a plane and of the one-point superconformal block on a torus. We also explicitly find the two-point global torus superconformal block in the necklace channel and check it against the Casimir differential equation. [ABSTRACT FROM AUTHOR]

We systematically explore the space of renormalization group flows of four-dimensional N = 1 superconformal field theories (SCFTs) triggered by relevant deformations, as well as by coupling to free chiral multiplets with relevant operators. In this way, we classify all possible fixed point SCFTs that can be obtained from certain rank 1 and 2 supersymmetric gauge theories with small amount of matter multiplets, identifying 7,346 inequivalent fixed points which pass a series of non-trivial consistency checks. This set of fixed points exhibits interesting statistical behaviors, including a narrow distribution of central charges (a, c), a correlation between the number of relevant operators and the ratio a/c, and trends in the lightest operator dimension versus a/c. The ratio a/c of this set is distributed between 0.7228 and 1.2100, where the upper bound is larger than that of previously known interacting SCFTs. Moreover, we find a plethora of highly non-perturbative phenomena, such as (super)symmetry enhancements, operator decoupling, non-commuting renormalization group flows, and dualities. We especially identify amongst these fixed points a new SCFT that has smaller central charges a c = 633 2000 683 2000 than that of the deformed minimal Argyres-Douglas theory, as well as novel Lagrangian duals for certain N = 1 deformed Argyres-Douglas theories. We provide a website to navigate through our set of fixed points. [ABSTRACT FROM AUTHOR]

Abstract Shadow formalism is a technique in two-dimensional CFT allowing straightforward computation of conformal blocks in the limit of infinitely large central charge. We generalize the construction of shadow operator for superconformal field theories. We demonstrate that shadow formalism yields known expressions for the large-c limit of the four-point superconformal block on a plane and of the one-point superconformal block on a torus. We also explicitly find the two-point global torus superconformal block in the necklace channel and check it against the Casimir differential equation.

Abstract We systematically explore the space of renormalization group flows of four-dimensional N $$ \mathcal{N} $$ = 1 superconformal field theories (SCFTs) triggered by relevant deformations, as well as by coupling to free chiral multiplets with relevant operators. In this way, we classify all possible fixed point SCFTs that can be obtained from certain rank 1 and 2 supersymmetric gauge theories with small amount of matter multiplets, identifying 7,346 inequivalent fixed points which pass a series of non-trivial consistency checks. This set of fixed points exhibits interesting statistical behaviors, including a narrow distribution of central charges (a, c), a correlation between the number of relevant operators and the ratio a/c, and trends in the lightest operator dimension versus a/c. The ratio a/c of this set is distributed between 0.7228 and 1.2100, where the upper bound is larger than that of previously known interacting SCFTs. Moreover, we find a plethora of highly non-perturbative phenomena, such as (super)symmetry enhancements, operator decoupling, non-commuting renormalization group flows, and dualities. We especially identify amongst these fixed points a new SCFT that has smaller central charges a c = 633 2000 683 2000 $$ \left(a,c\right)=\left(\frac{633}{2000},\frac{683}{2000}\right) $$ than that of the deformed minimal Argyres-Douglas theory, as well as novel Lagrangian duals for certain N $$ \mathcal{N} $$ = 1 deformed Argyres-Douglas theories. We provide a website https://qft.kaist.ac.kr/landscape to navigate through our set of fixed points.

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 It was recently shown that 3d N $$ \mathcal{N} $$ = 1 supersymmetric Wess-Zumino models can be studied in the ϵ-expansion by analytically continuing the number of fermionic degrees of freedom to be half-integer. In this work we study the extension of this strategy to gauge theories. We consider U(1) gauge theories with N g neutral Majorana fermions χ a , N f charge-1 bosons ϕ i and N f × N g charge-1 Dirac fermions ψ ia in the d = 4 − 2ϵ expansion. Analytically continuing to N g = 1 2 $$ \frac{1}{2} $$ schematically matches the Lagrangian and matter content of 3d N $$ \mathcal{N} $$ = 1 SQED, and we check whether this match can be made rigorous. We compute anomalous dimensions of χ a up to two loops and of meson operators up to one loop at the fixed points, and compare to expectations from SUSY. While we find obstructions to SUSY at small N f , at large N f the observables approach the expected values at a SUSY fixed point. This may allow for checks of 3d N $$ \mathcal{N} $$ = 1 IR dualities between gauge theories.

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 We study the worldsheet CFTs of type II strings on compact G 2 orbifolds obtained as quotients of a product of a Calabi-Yau threefold and a circle. For such models, we argue that the Calabi-Yau mirror map implies a mirror map for the associated G 2 varieties by examining how anti-holomorphic involutions behave under Calabi-Yau mirror symmetry. The mirror geometries identified by the worldsheet CFT are consistent with earlier proposals for twisted connected sum G 2 manifolds.

Abstract The Batalin-Vilkovisky formalism is applied to quantise the N $$ \mathcal{N} $$ = 1 supersymmetric generalisation of the Freedman-Townsend (FT) model, which was proposed by Lindström and Roček in 1983 in Minkowski superspace and is lifted to a supergravity background in this paper. This super FT theory describes a non-Abelian tensor multiplet and is known to be classically equivalent to a supersymmetric nonlinear sigma model. Using path integral considerations, we demonstrate that this equivalence holds at the quantum level in the sense that the quantum supercurrents in the two theories coincide. A modified Faddeev-Popov procedure is employed to quantise models for the N $$ \mathcal{N} $$ = 2 tensor multiplet in harmonic superspace. The obtained results agree with those derived by applying the Batalin-Vilkovisky scheme within the harmonic superspace setting.

Abstract We show that supersymmetry can be used to compute the BCFT one-point function coefficients for chiral primary operators, in 4d N $$ \mathcal{N} $$ = 2 SCFTs with 1 2 $$ \frac{1}{2} $$ -BPS boundary conditions. The main ingredient is the hemisphere partition function, with the boundary condition on the equatorial S 3. A supersymmetric Ward identity relates derivatives with respect to the chiral coupling constants to the insertion of the primaries at the pole of the hemisphere. Exact results for the one-point functions can be then obtained in terms of the localization matrix model. We discuss in detail the example of the super Maxwell theory in the bulk, interacting with 3d N $$ \mathcal{N} $$ = 2 SCFTs on the boundary. In particular we derive the action of the SL(2,ℤ) duality on the one-point functions.

Abstract Multi-parameter families of N $$ \mathcal{N} $$ = 0 Type IIA and Type IIB AdS5 solutions are presented, promoting to N $$ \mathcal{N} $$ = 1 in some special cases. The G-Structure description of each N $$ \mathcal{N} $$ = 1 solution is given, requiring an Abelian T-Duality of the G-Structure conditions and Pure Spinors. Investigations at the boundaries are performed for a two-parameter family of Type IIA and a three-parameter family of Type IIB solutions, finding the presence of orbifold singularities in some backgrounds. All parameters drop out of the Holographic Central Charge calculation, pointing to marginal deformations in the dual CFT description.

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 Classically, the ground states of N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory on ℝ × S 3/Γ where Γ is a discrete ADE subgroup of SU(2) are represented by flat Wilson lines winding around the ADE singularity. By a duality relating such ground states to WZW conformal blocks, the ground state degeneracy cannot be lifted by quantum corrections. Using the superconformal index, we compute the supersymmetric Casimir energy of each flat Wilson line for SU(2) SYM on different ADE singularities and find that the flat Wilson lines all have the same supersymmetric Casimir energy. We argue that this exact degeneracy is peculiar to N $$ \mathcal{N} $$ = 4 supersymmetry and show that the degeneracy is lifted when the number of supersymmetry is reduced. In particular, we uncover a surprising result for the ground state structure of the conformal N $$ \mathcal{N} $$ = 2 SU(2) four-flavor theory on S 3/Γ. For N $$ \mathcal{N} $$ = 4 SYM, S-duality maps the ground state Wilson lines to ground state t’ Hooft lines taking values in the Langlands dual group. We show that the supersymmetric Casimir energy of the t’ Hooft line ground states is the same as the Wilson line ground states. This can be viewed as a ground state test of S-duality.

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 Exact expressions for certain integrated correlators of four half-BPS operators in N $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory with gauge group SU(N) have been recently obtained thanks to a beautiful interplay between supersymmetric localisation and modular invariance. The large-N expansion at fixed Yang-Mills coupling of such integrated correlators produces an asymptotic series of perturbative terms, holographically related to higher derivative interactions in the low energy expansion of the type IIB effective action, as well as exponentially suppressed corrections at large N, interpreted as contributions from coincident (p, q)-string world-sheet instantons. In this work we define a manifestly modular invariant Borel resummation of the perturbative large-N expansion of these integrated correlators, from which we extract the exact non-perturbative large-N sectors via resurgence analysis. Furthermore, we show that in the ’t Hooft limit such modular invariant non-perturbative completions reduce to known resurgent genus expansions. Finally, we clarify how the same non-perturbative data is encoded in the decomposition of the integrated correlators based on SL(2, ℤ) spectral theory.

Abstract In this paper we revisit the S 1 reduction of 4d N $$ \mathcal{N} $$ = 1 gauge theories, considering a double scaling on the radius of the circle and on the real masses arising from the global symmetries in the compactification. We discuss the implication of this double scaling for SQCD with gauge algebra of ABCD type. We then show how our prescription translates in the reduction of the 4d superconformal index to the 3d squashed three sphere partition function. This allows us to derive the expected integral identities for the 3d dualities directly from the four dimensional ones. This is relevant for the study of orthogonal SQCD, where the derivation from the 4d index is not possible in absence of the double scaling, because of a divergence due to a flat direction in the Coulomb branch of the effective theory on the circle. Furthermore, we obtain, for the even orthogonal case, a 3d duality with a quadratic fundamental monopole superpotential already discussed in the literature, that receives in this way an explanation from 4d.

Abstract We continue our analysis of bad theories initiated in [1], focusing on quiver theories with bad unitary and special unitary gauge groups in three dimensions. By extending the dualization algorithm we prove that the partition function of bad linear quivers can be written as a distribution, given by a sum of terms involving a product of delta functions times the partition function of a good quiver theory. We describe in detail the good quiver theories appearing in the partition function of the bad theory and discuss the brane interpretation of our result. We also discuss in detail the lift of these theories to 4d quivers with symplectic gauge groups, in which our results can be recovered by studying the Higgsing triggered by the expectation value for certain chiral operators. The paper is accompanied by a Mathematica file which implements the algorithm for an arbitrary unitary bad linear quiver.

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 We use freely acting asymmetric orbifolds of type IIB string theory to construct a class of theories in five dimensions with eight supercharges whose moduli spaces for vector multiplets and hypermultiplets can be determined exactly. We argue that no quantum corrections to these moduli spaces arise. We focus on examples in which all moduli are in the NS-NS sector, while all fields from the R-R sector become massive. The full symmetry group of the moduli space is then determined by the subgroup of the T-duality group that survives the orbifold action. We illustrate this for freely acting orbifolds of type IIB string theory on T 5 with 0, 1 or 2 hypermultiplets.

Abstract We present higher-derivative deformations of the ModMax theory which preserve both U(1) duality symmetry and Weyl invariance. In particular, we single out a class of deformations expected to describe a low-energy effective action for the ModMax theory. We also elaborate on (higher-derivative) deformations of the N $$ \mathcal{N} $$ = 1 super ModMax theory.

Abstract In this paper we propose a physical derivation of a 4d conjectural duality for USp(2N) with an anti-symmetric rank-two tensor and fundamental flavors, in presence of a non-trivial superpotential. This duality has been conjectured as a consequence of an exact identity between the superconformal indices of the two phases, proved in the mathematical literature. Here we show that the duality can be derived by a combined sequence of known dualities, deconfinement of tensor matter, RG flow and Higgsing. Furthermore, by following these steps on the superconformal index, we provide an alternative derivation of the integral identity as well.

Abstract We study the geometries obtained by performing super non-Abelian T-duality of the Principal Chiral Model on OSp(1|2). While the initial model represents an appropriate 3D supergravity background, interpretable as the superspace version of AdS3, the T-dual model fails solving the 3D supergravity torsion constraints. We argue that this has to do with a factorisation pattern taking place under dualisation: the dual 3D geometry can be rewritten as the supersymmetric version of AdS2, satisfying the supergravity constraints, fibered over what we interpret as the superspace equivalent of the standard bosonic line. We discuss an interesting connection between T-duals of generic Principal Chiral Models and Poisson sigma models. We exploit it to show that in a suitable limit the dual action studied in this work gives rise to JT (super)gravity.

Abstract We conjecture a set of differential equations that characterizes the Liouville irregular states of half-integer ranks, which extends the generalized AGT correspondence to all the (A 1 , A even) and (A 1 , D odd) types Argyres-Douglas theories. For lower half-integer ranks, our conjecture is verified by deriving it as a suitable limit of a similar set of differential equations for integer ranks. This limit is interpreted as the 2D counterpart of a 4D RG-flow from (A 1 , D 2n ) to (A 1 , D 2n−1). For rank 3/2, we solve the conjectured differential equations and find a power series expression for the irregular state |I (3/2)〉. For rank 5/2, our conjecture is consistent with the differential equations recently discovered by H. Poghosyan and R. Poghossian.

Abstract The Seiberg-Witten solution to four-dimensional N $$ \mathcal{N} $$ = 2 super-Yang-Mills theory with gauge group SU(N) and without hypermultiplets is used to investigate the neighborhood of the maximal Argyres-Douglas points of type a 1 a N − 1 $$ \left({\mathfrak{a}}_1,{\mathfrak{a}}_{N-1}\right) $$ . A convergent series expansion for the Seiberg-Witten periods near the Argyres-Douglas points is obtained by analytic continuation of the series expansion around the ℤ 2N symmetric point derived in arXiv:2208.11502. Along with direct integration of the Picard-Fuchs equations for the periods, the expansion is used to determine the location of the walls of marginal stability for SU(3). The intrinsic periods and Kähler potential of the a 1 a N − 1 $$ \left({\mathfrak{a}}_1,{\mathfrak{a}}_{N-1}\right) $$ superconformal fixed point are computed by letting the strong coupling scale tend to infinity. We conjecture that the resulting intrinsic Kähler potential is positive definite and convex, with a unique minimum at the Argyres-Douglas point, provided only intrinsic Coulomb branch operators with unitary scaling dimensions ∆ > 1 acquire a vacuum expectation value, and provide both analytical and numerical evidence in support of this conjecture. In all the low rank examples considered here, it is found that turning on moduli dual to ∆ ≤ 1 operators spoils the positivity and convexity of the intrinsic Kähler potential.

We continue our analysis of bad theories initiated in [1], focusing on quiver theories with bad unitary and special unitary gauge groups in three dimensions. By extending the dualization algorithm we prove that the partition function of bad linear quivers can be written as a distribution, given by a sum of terms involving a product of delta functions times the partition function of a good quiver theory. We describe in detail the good quiver theories appearing in the partition function of the bad theory and discuss the brane interpretation of our result. We also discuss in detail the lift of these theories to 4d quivers with symplectic gauge groups, in which our results can be recovered by studying the Higgsing triggered by the expectation value for certain chiral operators. The paper is accompanied by a Mathematica file which implements the algorithm for an arbitrary unitary bad linear quiver. [ABSTRACT FROM AUTHOR]

In this paper we revisit the S1 reduction of 4d N = 1 gauge theories, considering a double scaling on the radius of the circle and on the real masses arising from the global symmetries in the compactification. We discuss the implication of this double scaling for SQCD with gauge algebra of ABCD type. We then show how our prescription translates in the reduction of the 4d superconformal index to the 3d squashed three sphere partition function. This allows us to derive the expected integral identities for the 3d dualities directly from the four dimensional ones. This is relevant for the study of orthogonal SQCD, where the derivation from the 4d index is not possible in absence of the double scaling, because of a divergence due to a flat direction in the Coulomb branch of the effective theory on the circle. Furthermore, we obtain, for the even orthogonal case, a 3d duality with a quadratic fundamental monopole superpotential already discussed in the literature, that receives in this way an explanation from 4d. [ABSTRACT FROM AUTHOR]

We use freely acting asymmetric orbifolds of type IIB string theory to construct a class of theories in five dimensions with eight supercharges whose moduli spaces for vector multiplets and hypermultiplets can be determined exactly. We argue that no quantum corrections to these moduli spaces arise. We focus on examples in which all moduli are in the NS-NS sector, while all fields from the R-R sector become massive. The full symmetry group of the moduli space is then determined by the subgroup of the T-duality group that survives the orbifold action. We illustrate this for freely acting orbifolds of type IIB string theory on T5 with 0, 1 or 2 hypermultiplets. [ABSTRACT FROM AUTHOR]

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 FROM AUTHOR]

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 S3 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 ̂ 3 or D ̂ 3 quiver theories, and the equality of these quiver theories, which comes from A ̂ 3 = 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 FROM AUTHOR]

Exact expressions for certain integrated correlators of four half-BPS operators in N = 4 supersymmetric Yang-Mills theory with gauge group SU(N) have been recently obtained thanks to a beautiful interplay between supersymmetric localisation and modular invariance. The large-N expansion at fixed Yang-Mills coupling of such integrated correlators produces an asymptotic series of perturbative terms, holographically related to higher derivative interactions in the low energy expansion of the type IIB effective action, as well as exponentially suppressed corrections at large N, interpreted as contributions from coincident (p, q)-string world-sheet instantons. In this work we define a manifestly modular invariant Borel resummation of the perturbative large-N expansion of these integrated correlators, from which we extract the exact non-perturbative large-N sectors via resurgence analysis. Furthermore, we show that in the ’t Hooft limit such modular invariant non-perturbative completions reduce to known resurgent genus expansions. Finally, we clarify how the same non-perturbative data is encoded in the decomposition of the integrated correlators based on SL(2, ℤ) spectral theory. [ABSTRACT FROM AUTHOR]

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 S3 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 ̂ 3 or D ̂ 3 quiver theories, and the equality of these quiver theories, which comes from A ̂ 3 = 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 FROM AUTHOR]

In this paper we propose a physical derivation of a 4d conjectural duality for USp(2N) with an anti-symmetric rank-two tensor and fundamental flavors, in presence of a non-trivial superpotential. This duality has been conjectured as a consequence of an exact identity between the superconformal indices of the two phases, proved in the mathematical literature. Here we show that the duality can be derived by a combined sequence of known dualities, deconfinement of tensor matter, RG flow and Higgsing. Furthermore, by following these steps on the superconformal index, we provide an alternative derivation of the integral identity as well. [ABSTRACT FROM AUTHOR]

We present higher-derivative deformations of the ModMax theory which preserve both U(1) duality symmetry and Weyl invariance. In particular, we single out a class of deformations expected to describe a low-energy effective action for the ModMax theory. We also elaborate on (higher-derivative) deformations of the N = 1 super ModMax theory. [ABSTRACT FROM AUTHOR]

We study the geometries obtained by performing super non-Abelian T-duality of the Principal Chiral Model on OSp(1|2). While the initial model represents an appropriate 3D supergravity background, interpretable as the superspace version of AdS3, the T-dual model fails solving the 3D supergravity torsion constraints. We argue that this has to do with a factorisation pattern taking place under dualisation: the dual 3D geometry can be rewritten as the supersymmetric version of AdS2, satisfying the supergravity constraints, fibered over what we interpret as the superspace equivalent of the standard bosonic line. We discuss an interesting connection between T-duals of generic Principal Chiral Models and Poisson sigma models. We exploit it to show that in a suitable limit the dual action studied in this work gives rise to JT (super)gravity. [ABSTRACT FROM AUTHOR]

We conjecture a set of differential equations that characterizes the Liouville irregular states of half-integer ranks, which extends the generalized AGT correspondence to all the (A1, Aeven) and (A1, Dodd) types Argyres-Douglas theories. For lower half-integer ranks, our conjecture is verified by deriving it as a suitable limit of a similar set of differential equations for integer ranks. This limit is interpreted as the 2D counterpart of a 4D RG-flow from (A1, D2n) to (A1, D2n−1). For rank 3/2, we solve the conjectured differential equations and find a power series expression for the irregular state |I(3/2)〉. For rank 5/2, our conjecture is consistent with the differential equations recently discovered by H. Poghosyan and R. Poghossian. [ABSTRACT FROM AUTHOR]

The Seiberg-Witten solution to four-dimensional N = 2 super-Yang-Mills theory with gauge group SU(N) and without hypermultiplets is used to investigate the neighborhood of the maximal Argyres-Douglas points of type a 1 a N − 1 . A convergent series expansion for the Seiberg-Witten periods near the Argyres-Douglas points is obtained by analytic continuation of the series expansion around the ℤ2N symmetric point derived in arXiv:2208.11502. Along with direct integration of the Picard-Fuchs equations for the periods, the expansion is used to determine the location of the walls of marginal stability for SU(3). The intrinsic periods and Kähler potential of the a 1 a N − 1 superconformal fixed point are computed by letting the strong coupling scale tend to infinity. We conjecture that the resulting intrinsic Kähler potential is positive definite and convex, with a unique minimum at the Argyres-Douglas point, provided only intrinsic Coulomb branch operators with unitary scaling dimensions ∆ > 1 acquire a vacuum expectation value, and provide both analytical and numerical evidence in support of this conjecture. In all the low rank examples considered here, it is found that turning on moduli dual to ∆ ≤ 1 operators spoils the positivity and convexity of the intrinsic Kähler potential. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider the spin-2 field perturbations of four families of supergravity solutions. These include AdS5 and AdS7 backgrounds of type IIA as well as AdS4 and AdS6 backgrounds of Type IIB. As the main result, we show that, in all the cases, there is a solution given by a combination of the warp factors. We also find the respective mass spectra. We analyze the normalizability of the solutions and identify the superconformal multiplets dual to them.

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 explore the quantum algebraic formalism of the gauge origami system in ℂ 4, where D2/D4/D6/D8-branes are present. We demonstrate that the contour integral formulas have free field interpretations, leading to the operator formalism of qq-characters associated with each D-brane. The qq-characters of D2 and D4-branes correspond to screening charges and generators of the affine quiver W-algebra, respectively. On the other hand, the qq-characters of D6 and D8-branes represent novel types of qq-characters, where monomial terms are characterized by plane partitions and solid partitions. The composition of these qq-characters yields the instanton partition functions of the gauge origami system, eventually establishing the BPS/CFT correspondence. Additionally, we demonstrate that the fusion of qq-characters of D-branes in lower dimensions results in higher-dimensional D-brane qq-characters. We also investigate quadratic relations among these qq-characters. Furthermore, we explore the relationship with the representations, q-characters, and the Bethe ansatz equations of the quantum toroidal gl 1 $$ {\mathfrak{gl}}_1 $$ . This connection provides insights into the Bethe/Gauge correspondence of the gauge origami system from both gauge-theoretic and quantum-algebraic perspectives. We finally present conjectures regarding generalizations to general toric Calabi-Yau four-folds. These generalizations imply the existence of an extensive class of qq-characters, which we call BPS qq-characters. These BPS qq-characters offer a new systematic approach to derive a broader range of BPS/CFT correspondence and Bethe/Gauge correspondence.

Abstract In this paper we give a field theory explanation of two confining dualities that have been proposed in the literature based on exact results from supersymmetric localization. The first confining model under investigation is 4d SU(N c + 1) SQCD with a conjugate rank-2 anti-symmetric tensor, N c + 3 anti-fundamentals, 2N c fundamentals and a superpotential that couples the anti-symmetric tensor and the fundamentals. The second confining model studied here is 3d N $$ \mathcal{N} $$ = 2 USp(4) gauge SQCD with two fundamentals, two rank-2 anti-symmetric tensors and vanishing superpotential. Here we prove that these models are confining by using the technique of deconfining the anti-symmetric tensors and then by flowing to the IR description by sequential dualities. As a bonus the analysis provides (alternative) proofs of the identities obtained from supersymmetric localization.

Abstract Partially motivated by the fact that the grand partition function of the ABJM theory or its generalization is expressed by a spectral operator enjoying symmetries of the Weyl group, it was found that the grand partition function satisfies the q-Painlevé equation, which is constructed from the affine Weyl group. In this paper we clarify the affine symmetries of the grand partition function. With the affine symmetries, we find that the grand partition function extends naturally outside the fundamental domain of duality cascades and once the Painlevé equation holds in the fundamental domain, so does it outside.

Abstract In this paper, we perform a systematic and analytical exploration of de Sitter conditions in type IIA compactifications with (non-)geometric fluxes along with the standard NS-NS and RR p-form fluxes. Exploiting the fact that the F-term scalar potential can be written as a bilinear form, we start by studying the most generic case. We find four conditions that the scalar fields and fluxes must satisfy to achieve de Sitter vacua. Particularizing to different configurations, we recover and extend previous results in the literature. We then impose an Ansatz in which the F-terms are proportional to the respective Kähler derivatives. In this set-up we are able to derive additional constraints and to classify the possible dS no-go scenarios in terms of eight axionic fluxes. Individually considering that any of these fluxes can be vanishing or non-vanishing leads to a total of 256 flux configurations. We find that 227 of these 256 possibilities result in a dS no-go scenario. The remaining 29 flux configurations, a priori, do not lead to dS no-go cases and would deserve further investigation.

Abstract We consider two dimensional (2D) gauged linear sigma models (GLSMs) with (0, 2) supersymmetry and U(1) gauge group which posses global symmetries. We distinguish between two cases: one obtained as a reduction from the (2, 2) supersymmetric GLSM and another not coming from a reduction. In the first case we find the Abelian T-dual, comparing with previous studies. Then, the Abelian T-dual model of the second case is found. Instanton corrections are also discussed in both situations. We explore the vacua for the scalar potential and we analyse the target space geometry of the dual model. An example with gauge symmetry U(1) × U(1) is discussed, which posses non-Abelian global symmetry. Non-Abelian T-dualization of U(1) (0, 2) 2D GLSMs is implemented for models that arise as a reduction from the (2, 2) case; we study a model with U(1) gauge symmetry and SU(2) global symmetry. It is shown that for a positive definite scalar potential, the dual vacua to $${\mathbb{P}}^{1}$$ constitutes a disk. Instanton corrections to the superpotential are obtained and are shown to be encoded in a shift of the holomorphic function E. We conclude by analyzing an example with SU(2) × SU(2) global symmetry, obtaining that the space of dual vacua to $${\mathbb{P}}^{1}$$ × $${\mathbb{P}}^{1}$$ consists of two copies of the disk, also for the case of positive definite potential. Here we are able to fully integrate the equations of motion of non-Abelian T-duality, improving the analysis with respect to the studies in (2, 2) models.

Abstract We continue the survey initiated in [1] to explore the Bethe/Gauge correspondence between supersymmetric SO/Sp gauge theories in 2d/3d/4d and open spin chain with integrable boundaries. We collect the known Bethe ansatz equations of different types of spin chains with general boundaries that have been analyzed in the literature, and compare them with the vacua equations of the quiver gauge theories. It seems that not all the vacua equations of quiver gauge theory with BCD-type gauge groups can be realized as some known Bethe ansatz equations of integrable spin chain models.

Abstract We show that a large subclass of 3d N $$ \mathcal{N} $$ = 4 quiver gauge theories consisting of unitary and special unitary gauge nodes with only fundamental/bifundamental matter have multiple Seiberg-like IR duals. A generic quiver T $$ \mathcal{T} $$ in this subclass has a non-zero number of balanced special unitary gauge nodes and it is a good theory in the Gaiotto-Witten sense. We refer to this phenomenon as IR N-ality and the set of mutually IR dual theories as the N-al set associated with the quiver T $$ \mathcal{T} $$ . Starting from T $$ \mathcal{T} $$ , we construct a sequence of dualities by step-wise implementing a set of quiver mutations which act locally on the gauge nodes. The associated N-al theories can then be read off from this duality sequence. The quiver T $$ \mathcal{T} $$ generically has an emergent Coulomb branch global symmetry in the IR, such that the rank of the IR symmetry is always greater than the rank visible in the UV. We show that there exists at least one theory in the N-al set for which the rank of the IR symmetry precisely matches the rank of the UV symmetry. In certain special cases that we discuss in this work, the correct emergent symmetry algebra itself may be read off from this preferred theory (or theories) in addition to the correct rank. Finally, we give a recipe for constructing the 3d mirror associated with a given N-al set and show how the emergent Coulomb branch symmetry of T $$ \mathcal{T} $$ is realized as a UV-manifest Higgs branch symmetry of the 3d mirror. This paper is the second in a series of four papers on 3d N $$ \mathcal{N} $$ = 4 Seiberg-like dualities, preceded by the work [1].

Abstract We show that the bosonic sector of the N = (1, 0), 6D Salam-Sezgin gauged supergravity model possesses a T-duality symmetry upon a circle reduction to D = 5. We then construct a simple magnetic rotating string solution with two equal angular momenta. Applying the T-duality transformation to this solution, we obtain the general boosted rotating dyonic black string solutions whose global structures and thermodynamic quantities are also analyzed. Owing to the fact that the solutions are not asymptotically flat, we find that there are two distinct globally-different non-extremal solutions with two different sets of thermal dynamic variables, with both satisfying the thermodynamic first law and the corresponding Small relations. However, their BPS limit becomes the same and we show that it preserves one quarter of supersymmetry by directly solving the corresponding Killing spinor equations.

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 find new bilinear relations for the partition functions of the U(N) k × U(N + M) −k ABJ theory with two parameter mass deformation (m 1 , m 2), which generalize the $$\mathfrak{q}$$ -Toda-like equation found previously for m 1 = m 2. By combining the bilinear relations with the Seiberg-like dualities and the duality cascade relations, we can determine the exact values of the partition functions recursively with respect to N. This method is more efficient than the exact calculation by the standard TBA-like approach in the Fermi gas formalism. As an application we study the large N asymptotics of the partition function with the mass parameters in the supercritical regime where the large N expansion obtained for small mass parameters is invalid.

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]

In this paper, we consider the spin-2 field perturbations of four families of supergravity solutions. These include AdS5 and AdS7 backgrounds of type IIA as well as AdS4 and AdS6 backgrounds of Type IIB. As the main result, we show that, in all the cases, there is a solution given by a combination of the warp factors. We also find the respective mass spectra. We analyze the normalizability of the solutions and identify the superconformal multiplets dual to them. [ABSTRACT FROM AUTHOR]