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We consider the insertion of a Gukov-Witten surface defect in SU(N) N=4 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.

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 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 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 We evaluate the superconformal index of 4d N $$ \mathcal{N} $$ = 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.

We study the spindle compactification of families of AdS$_5$ consistent truncations corresponding to M5 branes wrapped on complex curves in Calabi-Yau three-folds. From the AdS/CFT correspondence these models are dual to $\mathcal{N}=1$ SCFTs obtained by gluing of $T_N$ blocks. The truncations considered here have both vector and hyper multiplets and the analysis of the BPS equations on the spindle allows to extract the central charges. Such analysis gives also consistency conditions for the existence of the solutions. The solutions are then found both analytically and numerically for opportune choices of the charges for some sub-families of truncations. We then compare our results with the one expected from the field theory side, by integrating the anomaly polynomial.

Abstract We study orientifold projections of families of four-dimensional N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ = 4 SYM. Our construction generalizes previous results on the orientifold projections of the PdP3b and PdP3c singularities.

Abstract 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 N $$ \mathcal{N} $$ = 4 SYM and for classes of N $$ \mathcal{N} $$ = 2 and N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ = 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.

Abstract 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.

Abstract The microstate counting of charged rotating AdS5 supersymmetric black holes has been reformulated in terms of an extremization problem, obtained from the superconformal index of the 4d dual SCFT. On the gravitational side this problem corresponds to the attractor mechanism of the theory KK reduced on AdS4. Such procedure has indeed been successfully applied to some consistent truncations with a known field theory dual description. In this paper we study the case of the Leigh-Strassler fixed point along these lines, finding an agreement between the field theory and the gravitational results.

Abstract We study dualities for 3d U(N c ) k chiral SQCD with D n+2-type superpotential, with n odd. We give a complete classification of such dualities in terms of the number of fundamentals and anti-fundamentals and the Chern-Simons level. The classification is obtained by real mass and Higgs flows from non-chiral dualities and we check the consistency of the new non-chiral dualities at the level of the partition function. We also check that the complex phases appearing in the integral identities between the partition functions are consistent with the contact terms computed as quantum corrections to the effective Chern-Simons level. The SU(N c ) k cases are recovered by gauging the topological symmetry from the U(N c ) dualities. Finally, we consider the case of USp(2N c )2k with two antisymmetric tensors and D n+2-type superpotential.

Abstract We study 3d 𝒩 = 2 dualities arising from the compactification of 4d 𝒩 = 1 Usp(2n) SQCD with two antisymmetric rank-two tensors and D k+2-type superpotential, with odd k. The analysis is carried out by using field theory methods and by checking the various steps on the three sphere partition function. Most of the results are based on a conjectural confining duality that we do not prove but that fits consistently with the web of dualities that we obtain. Along the analysis we recover dualities already claimed in the literature and we propose new ones. The final picture that emerges fits with the general scheme worked out for ordinary SQCD and for adjoint SQCD with A k -type superpotentials.

Abstract We study various orientifold projections of 4d N $$ \mathcal{N} $$ = 1 toric gauge theories, associated with CY singularities known as L a,b,a /ℤ2, with a + b even. We obtain superconformal chiral theories that have the same central charge, anomalies and superconformal index, whereas they were different before the orientifold. Some of these projections are implemented by a novel type of orientifold without fixed loci, known as glide orientifold. We claim that these theories flow to the same conformal manifold, and they are connected by quadratic exactly marginal deformations. The latter can be written in terms of conjugate pairs of bifundamental fields of R-charge one, generalizing previous results for unoriented non-chiral theories.

Abstract We compute τ RR minimization in gauged supergravity for M-theory and String Theory truncations with both massless and massive vector multiplets. We explicitly compute, as anticipated in [1], that massive vector fields at the vacuum require the introduction of a constraint through a Lagrange multiplier. We illustrate this explicitly in two examples, namely the U(1)2-invariant truncation dual to the mABJM model and the ISO(7) truncation in massive IIA, the latter being a theory with both electric and magnetic gauging. We revisit the vacuum constraints at AdS 4 and show how the supergravity analysis matches the results of the field theory dual computation.

In this note we elaborate on a recent counter-example to the Nelson-Seiberg theorem and to its generalizations. We provide sufficient conditions for the existence of such counter-examples, finding new ones. We claim that these counter-examples are connected with the presence of pairs of fields with opposite R-charge getting a VEV. Furthermore we comment on the “non-genericity” of our models, showing that none of them violates the original Nelson-Seiberg theorem.

We study 3d N=2 SQCD with symplectic and orthogonal gauge groups and adjoint matter. For USp(2n) with two fundamentals and SO(N) 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 USp(2n) 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.

Abstract We study 4d SCFTs obtained by orientifold projections on necklace quivers with fractional branes. The models obtained by this procedure are 𝒩 = 1 linear quivers with unitary, symplectic and orthogonal gauge groups, bifundamental and tensorial matter. Remarkably, models that are not dual in the unoriented case can have the same central charges and superconformal index after the projection. The reason for this behavior rests upon the ubiquitous presence of adjoint fields with R-charge one. We claim that the presence of such fields is at the origin of the notion of inherited S-duality on the models’ conformal manifold.

We classify the global one-form symmetries for non-Lagrangian $\mathcal{N}=3$ SCFTs that arise by the action of $S$-fold projections on D3-branes. Such a classification is dictated, on a generic point of the Coulomb branch, by probing the charge spectrum of $(p, q)$-strings in the brane setup. The charge lattice of lines is then obtained by finding the ones that are genuine modulo screening by dynamical particles. The one-form symmetries are then extracted from the maximal sub-lattices of mutually local lines. We further comment on the existence of non-invertible symmetries for some of these $\mathcal{N}=3$ SCFTs.

Abstract We study the Cardy-like limit of the superconformal index of generic N $$ \mathcal{N} $$ = 1 SCFTs with ABCD gauge algebra, providing strong evidence for a universal formula that captures the behavior of the index at finite order in the rank and in the fugacities associated to angular momenta. The formula extends previous results valid at lowest order, and generalizes them to generic SCFTs. We corroborate the validity of our proposal by studying several examples, beyond the well-understood toric class. We compute the index also for models without a weakly-coupled gravity dual, whose gravitational anomaly is not of order one.

Abstract We study the superconformal index of 4d N $$ \mathcal{N} $$ = 4 USp(2N c ) and SO(N c ) SYM from a matrix model perspective. We focus on the Cardy-like limit of the index. Both in the symplectic and orthogonal case the index is dominated by a saddle point solution which we identify, reducing the calculation to a matrix integral of a pure Chern-Simons theory on the three-sphere. We further compute the subleading logarithmic corrections, which are of the order of the center of the gauge group. In the USp(2N c ) case we also study other subleading saddles of the matrix integral. Finally we discuss the case of the Leigh-Strassler fixed point with SU(N c ) gauge group, and we compute the entropy of the dual black hole from the Legendre transform of the entropy function.

Abstract We study dualities for 3d N $$ \mathcal{N} $$ = 2 SU(N c ) SQCD at Chern-Simons level k in presence of an adjoint with polynomial superpotential. The dualities are dubbed chiral because there is a different amount of fundamentals N f and antifundamentals N a . We build a complete classification of such dualities in terms of |N f − N a | and k. The classification is obtained by studying the flow from the non-chiral case, and we corroborate our proposals by matching the three-sphere partition functions. Finally, we revisit the case of SU(N c ) SQCD without the adjoint, comparing our results with previous literature.

Abstract The additional data necessary to univocally fix the gauge group for a given algebra are represented by the same charge lattices of mutually local Wilson and ’t Hooft lines for both 4d N $$ \mathcal{N} $$ = 4 SYM and N $$ \mathcal{N} $$ = 2 elliptic models. Motivated by this equivalence in this paper we study the Lens space index of these N $$ \mathcal{N} $$ = 2 elliptic models. The index is indeed sensitive to the global properties and in the N $$ \mathcal{N} $$ = 4 case it is expected to coincide among S-dual models with different global properties, while it gives different results for models that lie in other S-duality orbits. Here by an explicit calculation we show that the same results hold for the N $$ \mathcal{N} $$ = 2 elliptic models as well.

We systematically study 3d N=2 dualities for U(Nc) gauge theories with different CS levels for the abelian and the non-abelian factors. We derive such dualities by a gauging/ungauging procedure on other known dualities and by adding an opportune CS contact term for the baryonic symmetry. This allows us to follow the various steps on the three sphere partition function, obtaining exact identities among the new dual phases proposed here. We apply the procedure to various cases, namely SQCD without and with adjoint, chiral dualities and some sporadic cases arising from the real mass flow of models with an E7×U(1) enhancement of the global symmetry.

It has recently been claimed that a Cardy-like limit of the superconformal index of 4d N=4 SYM accounts for the entropy function, whose Legendre transform corresponds to the entropy of the holographic dual AdS5 rotating black hole. Here we study this Cardy-like limit for N=1 toric quiver gauge theories, observing that the corresponding entropy function can be interpreted in terms of the toric data. Furthermore, for some families of models, we compute the Legendre transform of the entropy function, comparing with similar results recently discussed in the literature.

Abstract We construct several novel examples of 3d N = 2 models whose free energy scales as N 3/2 at large N . This is the first step towards the identification of field theories with an M-theory dual. Furthermore, we match the volumes extracted from the free energy with the ones computed from the Hilbert series. We perform a similar analysis for the 4d N = 1 parents of the 3d models, matching the volume extracted from the a central charge to that obtained from the Hilbert series. For some of the 4d models, we show the existence of a Sasaki-Einstein metric on the internal space of the candidate type IIB gravity dual.

Abstract We study 3d monopole quivers, theories with product gauge groups interacting through monopole superpotentials and we observe that they are a natural setup for the study of the spontaneous breaking of 3d N $$ \mathcal{N} $$ = 2 supersymmetry. We give evidence of this statement by studying various examples of increasing complexity, considering quivers that are mirror dual to Wess-Zumino models. These Wess-Zumino models, in opportune regimes of parameters, break supersymmetry in perturbatively controllable (meta)stable vacua.

Abstract We study various aspects of the 4d/3d reduction of N $$ \mathcal{N} $$ = 1 dualities involving USp(2N c ) gauge theories with 2N f fundamentals and one antisymmetric. We discuss the non-trivial role played by the monopole superpotentials in the reduction and obtain new 3d dualities for models with both symplectic and unitary gauge groups. For N f = 4 we observe interesting webs of dualities and symmetry enhancements, recovering and extending some results already appeared in the literature.

We study little string theory (LST) compactified on T2, partially breaking supersymmetry by a discrete T-duality twist acting on both the Kähler and the complex structure of the torus. This setup gives raise to 4d N=3 models and it can be performed in both the type IIA and type IIB LSTs. We comment on the relation with other constructions proposed in the literature.

Background: The incidence of autoimmune thyroid diseases (ATD) may vary with the beginning of reproductive function, although few reports differentiate the incidence before and during the onset of puberty, examining gender bias. We analyzed onset of ATD in a pediatric population to assess gender differences in onset age, disease subtype, pubertal status, autoimmune co-morbidity, family history and treatment, focusing on the interaction between gender and pubertal stage.Patients and methods: We retrospectively recorded 382 children and adolescents with ATD. In each patient physical examination was considered. The presence of other associated autoimmune diseases (AAD) and familial predisposition was also recorded.Results: Predominant prevalence was noted in females compared to males (p < 0.001), both in Hashimoto's diseases (HD or HT) and Graves' disease (GD) (p < 0.001). Mean age at diagnosis showed no significant difference between sexes (p > 0.05). A higher prevalence in pubertal subjects was noted compared to prepubertal (p < 0.001, particularly HT in early and GD in late pubertal stage), without sexes difference intra-(prepubertal vs. pubertal) and inter-puberty groups (prepubertal vs. early pubertal vs. late pubertal). Both in HT and in GD, the prevalence of autoimmune associated diseases (AAD) was higher in males compared to females (p = 0.04), with similar distribution according to the pubertal maturation. The familial predisposition was similarly distributed in both genders (p > 0.05) and into pubertal stages (p > 0.05).Conclusions: Females are more prone to develop ATD during puberty, earlier in HT than in GD. The effect of puberty is not different between genders, suggesting the role of additional factors other than hormones. The screening for detection of ATD is recommended in all patients with positive family history and other autoimmune diseases, mostly in males. Considerations of gender in pediatrics could be important to define pathogenic mechanisms of ATD and to help in early diagnosis and clinical management.

Abstract Aspects of three dimensional N $$ \mathcal{N} $$ = 2 gauge theories with monopole super-potentials and their dualities are investigated. The moduli spaces of a number of such theories are studied using Hilbert series. Moreover, we propose new dualities involving quadratic powers for the monopole superpotentials, for unitary, symplectic and orthogonal gauge groups. These dualities are then tested using the three sphere partition function and matching of the Hilbert series. We also provide an argument for the obstruction to the duality for theories with quartic monopole superpotentials.

We derive a geometric formulation of the 2d central charge cr from infinite families of 4d N=1 superconformal field theories topologically twisted on constant curvature Riemann surfaces. They correspond to toric quiver gauge theories and are associated to D3 branes probing five dimensional Sasaki–Einstein geometries in the AdS/CFT correspondence. We show that cr can be expressed in terms of the areas of the toric diagram describing the moduli space of the 4d theory, both for toric geometries with smooth and singular horizons. We also study the relation between a-maximization in 4d and c-extremization in 2d, giving further evidences of the mixing of the baryonic symmetries with the exact R-current in two dimensions.

Abstract Four dimensional N=2 $$ \mathcal{N}=2 $$ Argyres-Douglas theories have been recently conjectured to be described by N=1 $$ \mathcal{N}=1 $$ Lagrangian theories. Such models, once reduced to 3d, should be mirror dual to Lagrangian N=4 $$ \mathcal{N}=4 $$ theories. This has been numerically checked through the matching of the partition functions on the three sphere. In this article, we provide an analytic derivation for this result in the A 2n−1 case via hyperbolic hypergeometric integrals. We study the D 4 case as well, commenting on some open questions and possible resolutions. In the second part of the paper we discuss other integral identities leading to the matching of the partition functions in 3d dual pairs involving higher monopole superpotentials.