Kutasov-Schwimmer (KS) dualities involve a rank-2 field with a polynomial superpotential. We derive KS-like dualities via deconfinement, that is assuming only Seiberg-like dualities, which instead just involve fundamental matter. Our derivation is split into two main steps. The first step is the construction of two families of linear quivers with $\textit{p}$−1 nodes that confine into a rank-2 chiral field with degree-($\textit{p}$+1) superpotential. Such chiral field is an U($\textit{N}$) adjoint in 3d and an USp(2$\textit{N}$) antisymmetric in 4d. In the second step we use these linear quivers to derive, via deconfinement, in a relatively straightforward fashion, two classes of KS-like dualities: the Kim-Park duality for U($\textit{N}$) with adjoint in 3d and the Intriligator duality for USp(2$\textit{N}$) with antisymmetric in 4d. We also discuss the close relation of our 3d family of confining unitary quivers to the 4d $$ \mathcal{N} $$ = 2 $\textit{D}$ [SU($\textit{N}$)] SCFTs by circle compactification and various deformations.

Italy

Sergio Benvenuti

Riccardo Comi

Sara Pasquetti

United Kingdom

Matteo Sacchi

Deconfinements, Kutasov-Schwimmer dualities and $\textit{D}$

We consider 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 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   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 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   <math> <mi>S</mi> </math>  $$ \mathcal{S} $$ -dual brane setups are infrared dual. The 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 mirror dualities can be uplifted to 4d dualities with 4d improved bifundamentals connecting USp(2N) nodes.

Mirror dualities with four supercharges

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.

Simone Giacomelli

China

Chiung Hwang

Fabio Marino

Probing bad theories with the dualization algorithm. Part II.

Recently an algorithm to build SL(2, ℤ) duals, including mirror duals, of 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 quiver theories and their 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 uplift has been introduced. In this work we use this new tool to study the so-called bad theories. Our approach allows us to determine exactly indices/partition functions for generic values of fugacities/real mass and FI parameters revealing their surprising feature: the 4d index/3d partition function of a bad theory behaves as a sum of distributions rather than an ordinary function of the deformation parameters. We focus on the bad SQCD, with U(N  c ) gauge group in 3d and USp(2N  c ) in 4d, while in an upcoming paper we will consider linear quivers which, in the 3d case, have both unitary and special unitary bad nodes.

Probing bad theories with the dualization algorithm. Part I

Recently an algorithm to dualize a theory into its mirror dual has been proposed, both for 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 linear quivers and for their 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 uplift. This mimics the manipulations done at the level of the Type IIB brane setup that engineers the 3d theories, where mirror symmetry is realized as S-duality, but it is enirely field-theoretic and based on the application of genuine infra-red dualities that implement the local action of S-duality on the quiver. In this paper, we generalize the algorithm to the full duality group, which is SL(2, ℤ) in 3d and PSL(2, ℤ) in 4d. This also produces dualities for 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 3 theories with Chern-Simons couplings, some of which have enhanced   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 supersymmetry, and their new 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 counterpart. In addition, we propose three ways to study the RG flows triggered by possible VEVs appearing at the last step of the algorithm, one of which uses a new duality that implements the Hanany-Witten move in field theory.

South Korea

The SL(2, ℤ) dualization algorithm at work

We introduce an algorithm to piecewise dualize linear quivers into their mirror dual. The algorithm uses two basic duality moves and the properties of the <math><mrow><mi>S</mi></mrow></math>-wall which can all be derived by iterative applications of Seiberg-like dualities.

Rethinking mirror symmetry as a local duality on fields

It is an interesting question whether a given infra-red duality between quantum field theories can be explained in terms of other more elementary dualities. For example recently it has been shown that mirror dualities can be obtained by iterative applications of Seiberg-like dualities. In this paper we continue this line of investigation focusing on theories with tensor matter. In such cases one can apply the idea of deconfinement, which consists of trading the tensor matter for extra gauge nodes by means of a suitable elementary duality. This gives an auxiliary dual frame which can then be manipulated with further dualizations, in an iterative procedure eventually yielding an interesting dual description of the original theory. The sequential deconfinement technique has avatars in different areas of mathematical physics, such as the study of hypergeometric and elliptic hypergeometric integral identities or of 2d free field correlators. We discuss various examples in the context 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supersymmetric theories, which are related to elliptic hypergeometric integrals. These include a new self-duality involving a quiver theory which exhibits a non-trivial global symmetry enhancement to E 6.

Lea Bottini

Dualities from dualities: the sequential deconfinement technique

In this paper we present various 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 dualities involving theories obtained by gluing two E[USp(2N)] blocks via the gauging of a common USp(2N) symmetry with the addition of 2L fundamental matter chiral fields. For L = 0 in particular the theory has a quantum deformed moduli space with chiral symmetry breaking and its index takes the form of a delta-function. We interpret it as the Identity wall which identifies the two surviving USp(2N) of each E[USp(2N)] block. All the dualities are derived from iterative applications of the Intriligator-Pouliot duality. This plays for us the role of the fundamental duality, from which we derive all others. We then focus on the 3d version of our 4d dualities, which now involve the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 T[SU(N)] quiver theory that is known to correspond to the 3d S-wall. We show how these 3d dualities correspond to the relations S 2 = −1, S  −1 S = 1 and STS = T  −1 S  −1 T  −1 for the S and T generators of SL(2, ℤ). These observations lead us to conjecture that E[USp(2N)] can also be interpreted as a 4d S-wall.

4d S-duality wall and SL(2, ℤ) relations

We present various 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 theories enjoying IR global symmetry enhancement. The models we consider have the USp(2N) gauge group, 8 fundamental, one antisymmetric chirals and various numbers of gauge singlets. By suitably turning on superpotential deformations involving the singlets which break part of the UV symmetry we flow to SCFTs with E 6, SO(10), SO(9), SO(8) and F 4 IR global symmetry. We explain these patterns of symmetry enhancement following two arguments due to Razamat, Sela and Zafrir. The first one involves the study of the relations satisfied by marginal operators, while the second one relies on the existence of self-duality frames.

Flips, dualities and symmetry enhancements

We construct a family of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 theories that we call   <math> <msubsup> <mi>E</mi> <mi>ρ</mi> <mi>σ</mi> </msubsup> </math>  $$ {E}_{\rho}^{\sigma } $$ [USp(2N)] which exhibit a novel type of 4d IR duality very reminiscent of the mirror duality enjoyed by the 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4   <math> <msubsup> <mi>T</mi> <mi>ρ</mi> <mi>σ</mi> </msubsup> </math>  $$ {T}_{\rho}^{\sigma } $$ [SU(N)] theories. We obtain the   <math> <msubsup> <mi>E</mi> <mi>ρ</mi> <mi>σ</mi> </msubsup> </math>  $$ {E}_{\rho}^{\sigma } $$ [USp(2N)] theories from the recently introduced E[USp(2N )] theory, by following the RG flow initiated by vevs labelled by partitions ρ and σ for two operators transforming in the antisymmetric representations of the USp(2N) × USp(2N) IR symmetries of the E[USp(2N)] theory. These vevs are the 4d uplift of the ones we turn on for the moment maps of T[SU(N)] to trigger the flow to   <math> <msubsup> <mi>T</mi> <mi>ρ</mi> <mi>σ</mi> </msubsup> </math>  $$ {T}_{\rho}^{\sigma } $$ [SU(N)]. Indeed the E[USp(2N)] theory, upon dimensional reduction and suitable real mass deformations, reduces to the T[SU(N)] theory. In order to study the RG flows triggered by the vevs we develop a new strategy based on the duality webs of the T[SU(N)] and E[USp(2N)] theories.