Generalized Families of QFTs

TL;DR

This paper explores how generalized symmetries and their anomalies influence the renormalization group flows and infrared phases of quantum field theories, extending previous concepts to include complex symmetry structures.

Contribution

It generalizes family anomaly considerations to broken generalized and categorical symmetries, including higher-group and non-invertible symmetries, and studies their implications for IR phases.

Findings

Analyzed anomaly inflow and SymTFTs for generalized families of QFTs.

Applied family anomalies to understand IR phases of 4d QCD-like theories.

Extended the framework to include higher-group and non-invertible symmetries.

Abstract

RG flows and IR phases of QFTs can be constrained by generalized symmetries and their anomalies. Broken symmetries act on the space of coupling constants of families of theories, and can also have IR-constraining family anomalies. We generalize family anomaly considerations to cases of broken generalized/categorical symmetries, including higher-group and non-invertible symmetries. We consider the anomaly inflow and SymTFTs of such generalized families of QFTs, and their implications for RG flows and constraints on the IR phases. As examples, we apply family anomalies to study the IR phases of $4d$ QCD-like theories deformed by irrelevant, multi-fermion interactions.