Symmetry-resolved entanglement for excited states and two entangling intervals in AdS3/CFT2
Konstantin Weisenberger, Suting Zhao, Christian Northe, René Meyer
Abstract
A bstract We test the proposal of [1] 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 [1], 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 $$ \hat{\mathfrak{u}}{(1)}_k $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>u</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> <mml:msub> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> <mml:mi>k</mml:mi> </mml:msub> </mml:math> 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 $$ \hat{\mathfrak{u}}{(1)}_k $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>u</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> <mml:msub> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> <mml:mi>k</mml:mi> </mml:msub> </mml:math> Kac-Moody sector.