Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models

TL;DR

The work addresses how Rényi entropies decompose into symmetry sectors in 1+1D CFTs with non-Abelian symmetry by analyzing WZW models. The authors develop a charged-moment framework built from unspecialised characters of Kac-Moody algebras and project onto irreps using group-Haar orthogonality, yielding a universal leading equipartition across symmetry sectors. They derive a precise $O(L^0)$ correction depending on the representation dimension and reveal a universal $\log\log L$ term with coefficient $\tfrac{\dim(G)}{2}$, plus a center-saddle structure that refines the finite-size corrections. The results are explicit for SU(2)$_k$ and general for any compact simple group $G$, with detailed SU(N) examples that connect to group volumes, center structure, and Casimir eigenvalues; the framework opens avenues for holographic comparisons and extensions to finite temperature or massive deformations.

Abstract

We consider the problem of the decomposition of the Rényi entanglement entropies in theories with a non-abelian symmetry by doing a thorough analysis of Wess-Zumino-Witten (WZW) models. We first consider $SU(2)_k$ as a case study and then generalise to an arbitrary non-abelian Lie group. We find that at leading order in the subsystem size $L$ the entanglement is equally distributed among the different sectors labelled by the irreducible representation of the associated algebra. We also identify the leading term that breaks this equipartition: it does not depend on $L$ but only on the dimension of the representation. Moreover, a $\log\log L$ contribution to the Rényi entropies exhibits a universal form related to the underlying symmetry group of the model, i.e. the dimension of the Lie group.