Generalized symmetry constraints on deformed 4d (S)CFTs

TL;DR

This paper investigates how generalized symmetries constrain deformations of 4d superconformal and non-supersymmetric gauge theories, revealing anomalies, dualities, and obstructions to trivial gapping.

Contribution

It classifies supersymmetric gauge theories with one-form symmetries, analyzes their anomalies, and explores new dualities and constraints on deformations, including non-Lagrangian theories.

Findings

Identified mixed zero-form/one-form 't Hooft anomalies in classifying theories.

Found obstructions to trivial gapped phases due to anomalies.

Discovered a new duality involving gauged Argyres-Douglas theories.

Abstract

We explore the consequence of generalized symmetries in four-dimensional $\mathcal{N}=1$ superconformal field theories. First, we classify all possible supersymmetric gauge theories with a simple gauge group that have a nontrivial one-form symmetry and flows to a superconformal field theory. Upon identifying unbroken discrete zero-form symmetries from the ABJ anomaly, we find that many of these theories have mixed zero-form/one-form 't Hooft anomalies. Then we classify the relevant deformations of these SCFTs that preserve the anomaly. From this mixed anomaly together with the anomalies of the discrete zero-form symmetries, we find obstructions for the relevant deformations of these SCFTs to flow to a trivially gapped phase. We also study non-Lagrangian SCFTs formed by gauging copies of Argyres-Douglas theories and constrain their deformations. In particular, we explore a new duality between the diagonal gauging of two $\mathcal{D}_3(SU(N))$ theories and $SU(N)$ gauge theory with two adjoints. We also repeat our analysis for a host of non-supersymmetric gauge theories having nontrivial one-form symmetry including examples that appear to flow to Bank-Zaks type CFTs.