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

**Authors:** Arpit Das, Javier Molina-Vilaplana, Pablo Saura-Bastida  
**arXiv:** [2409.02162](https://arxiv.org/abs/2409.02162)  
**Date:** 2024-09-03  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2409.02162v1/

## Key points

- The paper focuses on entanglement entropy in $(1+1)$-d rational conformal field theories (RCFT) with categorical non-invertible symmetries.
- It explores the symmetry of entanglement in generalized twisted and anyonic charge sectors within the theory.
- The study defines generalized boundary dependent charged moments crucial for achieving symmetry resolution of the entanglement entropy.
- An observation is made regarding the breakdown of entanglement equipartition between different charged sectors at the next-to-leading order in the ultraviolet cutoff.
- The findings contribute to existing literature on symmetry-resolved measures in quantum field theory and generalized global symmetries.
- The research builds upon previous work on categorical-symmetry resolved entanglement in conformal field theory, enriching the discussion presented in this paper.

## Summary

The paper titled "Generalized Symmetry Resolution of Entanglement in CFT for Twisted and Anyonic sectors" presents a comprehensive analysis of the entanglement entropy (EE) in $(1+1)$-d rational conformal field theories (RCFT) with categorical non-invertible symmetries. The study focuses on resolving the symmetry of entanglement concerning the generalized twisted and anyonic charge sectors within the theory. These anyonic sectors correspond to the irreducible representations of a modular fusion category that defines the symmetry and can be elucidated through the $(2+1)$-d symmetry topological field theory (SymTFT), which encapsulates the symmetry characteristics of the CFT. One of the key contributions of this work is defining the corresponding generalized boundary dependent charged moments essential for achieving symmetry resolution of the entanglement entropy. This aspect stands out as a significant outcome of the research. Furthermore, unlike scenarios involving invertible symmetries, an interesting observation made in this study is related to the breakdown of entanglement equipartition between different charged sectors at the next-to-leading order in the ultraviolet cutoff. The findings presented in this paper build upon existing literature on symmetry-resolved measures in quantum field theory and generalized global symmetries. The exploration of generalized symmetries in condensed matter physics also provides a relevant backdrop for understanding and contextualizing these results. Moreover, previous research on categorical-symmetry resolved entanglement in conformal field theory further complements and enriches the discussion presented in this paper. Overall, by delving into intricate details regarding twisted and anyonic sectors within RCFTs, this paper contributes significantly to advancing our understanding of symmetry resolution in entanglement phenomena within theoretical frameworks such as conformal field theories. Incorporating diverse perspectives from quantum field theory, condensed matter physics, and related areas enhances the depth and breadth of insights provided by this research endeavor. The incorporation of these perspectives also highlights the interdisciplinary nature of this study.