Generalized symmetry constraints on deformed 4D SCFTs

We explore the consequence of generalized symmetries in four-dimensional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi mathvariant="script">N</a:mi><a:mo>=</a:mo><a:mn>1</a:mn></a:mrow></a:math> 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 Adler-Bell-Jackiw (ABJ) anomaly, we find that many of these theories have mixed zero-form or 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 <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msub><d:mi mathvariant="script">D</d:mi><d:mn>3</d:mn></d:msub><d:mo stretchy="false">(</d:mo><d:mi>S</d:mi><d:mi>U</d:mi><d:mo stretchy="false">(</d:mo><d:mi>N</d:mi><d:mo stretchy="false">)</d:mo><d:mo stretchy="false">)</d:mo></d:math> theories and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>S</k:mi><k:mi>U</k:mi><k:mo stretchy="false">(</k:mo><k:mi>N</k:mi><k:mo stretchy="false">)</k:mo></k:math> gauge theory with two adjoints. We also repeat our analysis for a host of nonsupersymmetric gauge theories having nontrivial one-form symmetry including examples that appear to flow to Bank-Zaks type CFTs.