IAS High Energy Theory Seminar

Abstract: Homotopy theory and category theory have the capability to provide many insights into the structure of quantum field theory. Using these tools 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. I will present a fundamental dichotomy among these anomalies: the first class of anomalies can always be realized by symmetric gapped states, while the second class 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.