Generalized Symmetry Resolution of Entanglement in CFT for Twisted and Anyonic sectors

TL;DR

This paper develops a comprehensive method to resolve entanglement entropy in 1+1D rational conformal field theories with non-invertible symmetries, revealing new features like the breakdown of entanglement equipartition.

Contribution

It introduces a generalized symmetry resolution framework for entanglement entropy in RCFTs with non-invertible symmetries, connecting to topological field theory and defining new charged moments.

Findings

Entanglement resolution with respect to twisted and anyonic sectors.

Breakdown of entanglement equipartition at next-to-leading order.

Connection between RCFT symmetries and (2+1)D topological field theory.

Abstract

A comprehensive symmetry resolution of the entanglement entropy (EE) in $(1+1)$-d rational conformal field theories (RCFT) with categorical non-invertible symmetries is presented. This amounts to symmetry resolving the entanglement with respect to the generalized twisted and anyonic charge sectors of the theory. The anyonic sectors label the irreducible representations of a modular fusion category defining the symmetry and can be understood through the $(2+1)$-d symmetry topological field theory (SymTFT) that encodes the symmetry features of the CFT. Using this, we define the corresponding generalized boundary dependent charged moments necessary for the symmetry resolution of the entanglement entropy, which is the main result of this work. Furthermore, contrary to the case of invertible symmetries, we observe the breakdown of entanglement equipartition between different charged sectors at the next-to-leading order in the ultraviolet cutoff.