A Generalized Crystalline Equivalence Principle

TL;DR

This paper proves a broad version of the crystalline equivalence principle, establishing an equivalence between TQFTs with spatial symmetry and those with internal symmetry, and introduces a classification of anomalies in this context.

Contribution

It generalizes the crystalline equivalence principle and provides a new framework for classifying anomalies in TQFTs with spatial and categorical symmetries.

Findings

Established an equivalence of categories for TQFTs with G-symmetry

Defined and classified anomalies in TQFTs with spatial symmetry

Extended anomaly classification to categorical symmetries

Abstract

We prove a general version of the crystalline equivalence principle which gives an equivalence of categories between a category of TQFTs defined on a generic space with $G$-symmetry, and a category of TQFTs with internal symmetry. We give a definition and classification of anomalies associated to TQFTs in the presence of spatial symmetry, which we then generalize to a definition of an anomaly for a categorical symmetry.