It has been recently shown that the celebrated SCFT /VOA correspondence can be bridged via three-dimensional field theories arising from a specific R-symmetry twisted circle reduction. We apply this twisted reduction to the ($\textit{A}$ $\textit{, A}$ ) and ($\textit{A}$ $\textit{, D}$ ) families of 4d $$ \mathcal{N}=2 $$ Argyres-Douglas SCFTs using their $$ \mathcal{N}=1 $$ Agarwal-Maruyoshi-Song Lagrangians. From ($\textit{A}$ $\textit{, A}$ ) we derive the Gang-Kim-Stubbs family of 3d $$ \mathcal{N}=2 $$ gauge theories with SUSY enhancement to $$ \mathcal{N}=4 $$ in the infrared, generalizing a recent derivation made in the special cases $\textit{n}$ = 1$\textit{,}$ 2. Topological twists of these theories are known to yield $\textit{semisimple}$ TQFTs supporting $\textit{rational}$ VOAs on holomorphic boundaries. From ($\textit{A}$ $\textit{, A}$ ), ($\textit{A}$ $\textit{, D}$ ), and ($\textit{A}$ $\textit{, D}$ ), we obtain three new infinite families of 3d $$ \mathcal{N}=2 $$ abelian gauge theories, all with monopole superpotentials, flowing to $$ \mathcal{N}=4 $$ SCFTs without Coulomb branch, but with the same non-trivial Higgs branch as the four-dimensional parent. Their topological A-twist yields $\textit{non-semisimple}$ TQFTs related to $\textit{logarithmic}$ VOAs such as $$ \hat{su}{(2)}_{-4/3} $$ .

Iran

Arash Ardehali

South Korea

Dongmin Gang

United States

Neville Rajappa

Matteo Sacchi

3d SUSY enhancement and non-semisimple TQFTs from four dimensions

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

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

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 there has been an increasing interest in the study of generalized symmetries in dimensions higher than two. This has lead to the discovery of various manifestations of generalized symmetries, notably higher-group and non-invertible symmetries, in four dimensions. In this paper we shall examine what happens to this structure when the 4d theory is compactified to lower dimensions, specifically to 3d and 2d, where we shall be mainly interested in generalized symmetry structures whose origin can be linked to mixed flavor-gauge anomalies. We discuss several aspects of the compactification, and in particular argue that under certain conditions the discussed generalized symmetry structure may trivialize in the infrared. Nevertheless, we show that even when this happens the presence of the 4d generalized symmetry structure may still leave an imprint on the low-energy theory in terms of additional ’t Hooft anomalies or by breaking part of the symmetry. We apply and illustrate this using known examples of compactifications from four dimensions, particularly, the reduction of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 U(N  c ) SQCD on a circle to 3d and on a sphere to 2d.

Japan

Emily Nardoni

Orr Sela

Israel

Gabi Zafrir

Yunqin Zheng

Dimensionally reducing generalized symmetries from (3+1)-dimensions

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

Much insight into the dynamics of quantum field theories can be gained by studying the relationship between field theories in different dimensions. An interesting observation is that when two theories are related by dimensional reduction on a compact surface, their ’t Hooft anomalies corresponding to continuous symmetries are also related: the anomaly polynomial of the lower-dimensional theory can be obtained by integrating that of the higher-dimensional one on the compact surface. Naturally, this relation only holds if both theories are even dimensional. This raises the question of whether similar relations can also hold for the case of anomalies in discrete symmetries, which might be true even in odd dimensions. The natural generalization to discrete symmetries is that the anomaly theories, associated with the lower and higher dimensional theories, would be related by reduction on the compact surface. We explore this idea for compactifications of 5d superconformal field theories (SCFTs) to 3d on Riemann surfaces with global-symmetry fluxes. In this context, it can be used both as a check for these compactification constructions and for discovering new anomalies in the 5d SCFTs. This opens the way to applying the same idea of dimensional reduction of the anomaly theory to more general types of compactifications.

5d to 3d compactifications and discrete anomalies

We propose new classes of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 S-confining gauge theories, with a simple gauge group, rank-two matter and cubic superpotentials. The gauge group can be symplectic, orthogonal or special unitary. In some cases we derive the dualities via the deconfinement technique that uses iteratively known, more fundamental, dualities. In the symplectic case we discuss the 3d reduction to a confining unitary gauge theory with monopole superpotential. This 3d S-confinement provides an understanding of a recently proposed 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 theory that flows to the conformal manifold of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM with SU(2n + 1) gauge group. The 3d perspective allows us to generalize this construction to another similar flow with supersymmetry enhancement: a 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 theory that flows to the conformal manifold of a 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 necklace theory with SU(2n + 1)3 gauge group.

Stephane Bajeot

S-confining gauge theories and supersymmetry enhancements

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.

The SL(2, ℤ) dualization algorithm at work

Many interesting phenomena in quantum field theory such as dualities and symmetry enhancements can be understood using higher dimensional constructions. In this paper, we study compactifications of the rank 1 5d Seiberg   <math> <msub> <mi>E</mi> <msub> <mi>N</mi> <mrow> <mi>f</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> </math>  $$ {E}_{N_{f+1}} $$  SCFTs to 3d on Riemann surfaces of genus g &gt; 1. We rely on the recent progress in the study of compactifications of 6d SCFTs to 4d and torus compactifications of 5d SCFTs to conjecture 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 theories corresponding to the reduction of said 5d SCFTs on three punctured spheres. These can then be used to build 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 models corresponding to compactifications on more general surfaces. The conjectured theories are tested by comparing their properties against those expected from the compactification picture.

Trinions for the 3d compactification of the 5d rank 1   <math> <msub> <mi>E</mi> <msub> <mi>N</mi> <mrow> <mi>f</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> </math>  $$ {E}_{N_{f+1}} $$  SCFTs

Mixed anomalies, higher form symmetries, two-group symmetries and non-invertible symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories. We study mixed anomalies involving discrete zero-form global symmetries, and possibly a one-form symmetry, in 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  ≥ 3 gauge theories using the superconformal index. The effectiveness of this method is demonstrated via several classes of theories, including Chern-Simons-matter theories, such as the U(1) k  gauge theory with hypermultiplets of diverse charges, the T (SU(N)) theory of Gaiotto-Witten, the theories with 𝔰𝔬(2N)2k  gauge algebra and hypermultiplets in the vector representation, and variants of the Aharony-Bergman-Jafferis (ABJ) theory with the orthosymplectic gauge algebra. Gauging appropriate global symmetries of some of these models, we obtain various interesting theories with non-invertible symmetries or two-group structures.