Craig Lawrie (DESY Hamburg)

Generalized symmetry constraints on deformed 4d (S)CFTs

In this talk, I present an approach to constraining the infrared behavior of gauge theories, both supersymmetric and non-supersymmetric, using the modern paradigm of generalized global symmetries together with 't Hooft anomaly matching. 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. Further, can determine what infrared physics (confining, gapped, gapless, topological, ...) is compatible with the symmetry structure, in each case. To conclude, I will comment on the generalization to gauge theories with “strongly-coupled matter”.