Categorical Anomaly Matching

TL;DR

This paper develops a new categorical framework using tensor functors and anomalous simple categories to characterize and quantify anomalies in non-invertible symmetries, enhancing understanding of RG flows in quantum systems.

Contribution

It introduces Anomalous Simple Categories (ASCies) and a tensor functor framework to systematically analyze anomalies in categorical symmetries, extending anomaly classification to non-invertible cases.

Findings

Framework applies to various spacetime dimensions.

Captures anomalies in non-invertible and higher-form symmetries.

Connects anomalies to RG interfaces via SymTFTs.

Abstract

Matching 't Hooft anomalies is a powerful tool for constraining the low-energy dynamics of quantum systems and their allowed renormalization group (RG) flows. For non-invertible (or categorical) symmetries, however, a key challenge has been the lack of a precise framework to characterize and quantify anomalies. We address this by identifying tensor functors between UV and IR symmetry categories as central to capturing these constraints. To this end, we introduce Anomalous Simple Categories (ASCies) as fundamental building blocks of categorical anomalies. A given symmetry category may support multiple ASCies, each encoding distinct anomalous features. These structures naturally arise in the context of the Symmetry Topological Field Theory (SymTFT), where tensor functors correspond to RG-interfaces between UV and IR SymTFTs, and ASCies are realized as particular such interfaces satisfying simple, universal criteria. We demonstrate the utility of this framework through examples involving anomalous 0-form, higher-form, and crucially, non-invertible symmetries in various spacetime dimensions.