High Energy Theory Seminar: Matthew Yu

Title: When do anomalous finite symmetries in (3+1)d enforce gaplessness? 

Abstract: I will explain a comprehensive framework for characterizing the infrared (IR) phases of a fermionic QFTs in (3+1)d, based on their quantum anomalies associated with a finite symmetry. We uncover a fundamental dichotomy among these anomalies: the first class of anomalies can always be realized by symmetric gapped states i.e. there exists a TQFT that saturates the anomaly. The second class of anomalies can never be realized by gapped states without breaking the given symmetry, establishing the phenomenon of symmetry-enforced gaplessness in these settings. Using the construction of symmetry extension afforded to us by new developments in fusion 2-categories, we construct the candidate gapped states that theories with the first class of anomalies can flow to in the IR. As an application, I will provide examples of concrete predictions for the candidate IR phases of (3+1)d gauge theories based on our results.