We propose 2d <math altimg='si1.svg'><mi mathvariant='script'>N</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo stretchy='false'>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo stretchy='false'>)</mo></math> dualities between <math altimg='si2.svg'><mi mathvariant='normal'>SU</mi><mo stretchy='false'>(</mo><mi>N</mi><mo stretchy='false'>)</mo></math> gauge theories with fundamental and antisymmetric chiral matter and Landau-Ginzburg theories with chiral and Fermi multiplets. Many of these dualities can be derived by topologically twisting 4d s-confining gauge theories on a two-sphere, with integer non-negative <italic>R</italic> charges. We provide various checks of the dualities, showing that they descend from more &#8220;basic&#8221; dualities, similarly to analogous derivations in higher dimensions. The proof is based on the fact that the antisymmetric tensors can be traded with <math altimg='si3.svg'><mi mathvariant='normal'>USp</mi><mo stretchy='false'>(</mo><mn>2</mn><mi>n</mi><mo stretchy='false'>)</mo></math> gauge theories with fundamental chirals, mimicking the higher dimensional mechanism known as tensor deconfinement. The quivers obtained in this way can be shown to be dual to LG models after applying other elementary &#8220;basic&#8221; dualities.

Italy

Antonio Amariti

Pietro Glorioso

Germany

Fabio Mantegazza

Davide Morgante

Andrea Zanetti

Dualities from dualities in 2d <math altimg='si1.svg'><mi mathvariant='script'>N</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo stretchy='false'>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo stretchy='false'>)</mo></math>

We consider the insertion of a Gukov-Witten surface defect in <math><mrow><mi>SU</mi></mrow><mo>(</mo><mi>N</mi><mo>)</mo></math> <math><mi>N</mi><mo>=</mo><mn>4</mn></math> SYM corresponding to a probe D3-brane in the holographic dual setup. The defect gives rise to a 4d-2d coupled system encoding the entropy of the dual perturbed black hole, which can be extracted from the corresponding Superconformal Index. Elaborating on previous studies, we refine the results using both a saddle-point and a Bethe-Ansatz approach. The consistency of our computation is corroborated by the complete agreement between the two results in the appropriate regime of fugacities. Eventually, the sub-leading structure, emerging from our analysis, provides a suggestive EFT interpretation for the addition of the defect to the 4d system, mirroring the behavior of the probe D3-brane in the gravity dual.

Cardy matches Bethe on the surface: A tale of a brane and a black hole

In this paper we revisit the S 1 reduction of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 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.

A double scaling for the 4d/3d reduction of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 dualities

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.

A new 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 duality from the superconformal index

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   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 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.

Sporadic dualities from tensor deconfinement

We evaluate the superconformal index of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM with gauge algebra so(2N  c  + 1) in the Cardy-like limit. We then study the relation with the results obtained for the S-dual usp(2N  c ), discussing the fate of S-duality in different regions of charges. We find that S-duality is preserved thanks to a non-trivial integral identity that relates the three sphere partition functions of pure 3d Chern-Simons gauge theories.

S-duality in the Cardy-like limit of the superconformal index

We study 3d <math><mi>N</mi><mo>=</mo><mn>2</mn></math> SQCD with symplectic and orthogonal gauge groups and adjoint matter. For <math><mi>U</mi><mi>S</mi><mi>p</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo></math> with two fundamentals and <math><mi>S</mi><mi>O</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> with one vector these models have been recently shown to s-confine. Here we corroborate the validity of this proposal by relating it to the confinement of <math><mi>U</mi><mi>S</mi><mi>p</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo></math> with four fundamentals and an antisymmetric tensor, using exact mathematical results coming from the analysis of the partition function on the squashed three-sphere. Our analysis allows us to conjecture new s-confining theories for a higher number of fundamentals and vectors, in presence of linear monopole superpotentials. We then prove the new dualities through a chain of adjoint deconfinements and s-confining dualities.

Simone Rota

3d SO/USp adjoint SQCD: s-confinement and exact identities

We study orientifold projections of families of four-dimensional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 toric quiver gauge theories. We restrict to quivers that have the unusual property of being associated with multiple periodic planar diagrams which give rise, in general, to inequivalent models. A suitable orientifold projection relates a subfamily of the latter by conformal duality. That is, there exist exactly marginal deformations that connect the projected models. The deformations take the form of a sign flip in some of the superpotential interactions, similarly to the β-deformation of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM. Our construction generalizes previous results on the orientifold projections of the PdP3b  and PdP3c  singularities.

Massimo Bianchi

Sweden

Marco Fazzi

Salvo Mancani

Fabio Riccioni

Multi-planarizable quivers, orientifolds, and conformal dualities

We compute the Lens space index for 4d supersymmetric gauge theories involving symplectic gauge groups. This index can distinguish between different gauge groups from a given algebra and it matches across theories related by supersymmetric dualities. We provide explicit calculations for   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM and for classes of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 and   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 Lagrangian quivers related by S-duality. In these cases the index matches across the S-dual phases, while models in different S-duality orbits have a different Lens index. We provide analogous computations for a 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 toric quiver gauge theory corresponding to a ℤ7 orbifold of ℂ3. This SU(n)7 gauge theory becomes interesting in the case of n = 2 because it is conformally dual to other two models, with symplectic and unitary gauge groups, bifundamentals and antisymmetric tensors. We explicitly check this triality at the level of the Lens space index.

Symplectic gauge group on the Lens space

We study the compactification of the 𝒩 = 2 AdS5 consistent truncation of the conifold, in presence of a Betti vector multiplet, on the spindle. We derive the BPS equations and solve them at the poles, computing the central charge for both the twist and the anti-twist class, turning on the magnetic charge associated to the baryonic symmetry. Then, in the anti-twist class, where there are choices of the quantized flux that give origin to a positive central charge, we numerically solve the BPS equations interpolating between the poles of the spindle. We conclude by comparing our results with the one obtained from the analysis of the dual field theory, finding an exact agreement.