On the resolution of categorical symmetries in (Non-) Unitary Rational CFTs

TL;DR

This paper derives a general formula for symmetry-resolved entanglement entropy in 2D Rational Conformal Field Theories, connecting it to modular data and exploring various boundary conditions and non-unitary cases.

Contribution

It provides a new, purely 2D RCFT-based formula for symmetry-resolved entanglement entropy applicable to diverse boundary conditions and non-unitary theories, without using SymTFT.

Findings

The formula matches explicit examples in RCFTs.

Symmetry resolution subtleties are discussed for categorical and invertible symmetries.

Extension to non-unitary RCFTs with Haagerup-Izumi data shows full agreement.

Abstract

We explore several aspects of the categorical symmetry-resolved entanglement entropy (SREE) in two-dimensional Rational Conformal Field Theories (RCFTs) and express it directly in terms of the modular data of the theory. Motivated by arXiv:2409.02806, we provide a general formula for SREE that applies to symmetric (weakly/strongly) and cloaking boundary conditions as well as for fusion rings with multiplicities without invoking any SymTFT construction, relying instead on a purely 2d RCFT analysis. We check the formula against several explicit examples. Additionally, we study symmetry resolution for both categorical and invertible symmetries in (non-)diagonal RCFTs and comment on the subtleties that arise in these cases. Finally, we extend our analysis to diagonal non-unitary RCFTs, focusing on theories with generalized Haagerup-Izumi modular data, and find full agreement with the given formula.