Symmetry-resolved entanglement for excited states and two entangling intervals in AdS${}_3$/CFT${}_2$

TL;DR

This paper investigates symmetry-resolved entanglement in excited states and two-interval configurations within AdS${}_3$/CFT${}_2$, confirming holographic predictions through CFT calculations and revealing entanglement equipartition across charge sectors.

Contribution

It provides a detailed holographic and conformal field theory analysis of symmetry-resolved entanglement for excited states and multiple intervals, extending previous proposals and clarifying the structure of the Hilbert space.

Findings

Confirmed holographic computations match CFT results at large central charge.

Found equipartition of entanglement among charge sectors in all cases studied.

Clarified the factorization of the Hilbert space into gravitational and Kac-Moody sectors.

Abstract

We test the proposal of arXiv:2012.11274 for the holographic computation of the charged moments and the resulting symmetry-resolved entanglement entropy in different excited states, as well as for two entangling intervals. Our holographic computations are performed in $U(1)$ Chern-Simons-Einstein-Hilbert gravity, and are confirmed by independent results in a conformal field theory at large central charge. In particular, we consider two classes of excited states, corresponding to charged and uncharged conical defects in AdS${}_3$. In the conformal field theory, these states are generated by the insertion of charged and uncharged heavy operators. We employ the monodromy method to calculate the ensuing four-point function between the heavy operators and the twist fields. For the two-interval case, we derive our results on the AdS and the conformal field theory side, respectively, from the generating function method of arXiv:2012.11274, as well as the vertex operator algebra. In all cases considered, we find equipartition of entanglement between the different charge sectors. We also clarify an aspect of conformal field theories with a large central charge and $\mathfrak{u}(1)_k$ Kac-Moody symmetry used in our calculations, namely the factorization of the Hilbert space into a gravitational Virasoro sector with large central charge, and a $\mathfrak{u}(1)_k$ Kac-Moody sector.