Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

Abstract

We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

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

“…[33][34][35] to the resolution of non-abelian symmetries. A last one is to identify the holographic dual of the symmetry-resolved entanglement entropy for theories with non-abelian symmetry and compare it with our results, as already done for the abelian case in [37].…”

“…The possibility of measuring in an experiment the internal symmetry structure of the entanglement [20][21][22][23] went together with new theoretical frameworks developed to address the same problem [24,25]. These progresses paved the way to study different symmetryresolved contributions in various theoretical contexts such as CFTs [24][25][26][27][28][29][30][31], free [32,34] and interacting integrable quantum field theories [33,35], holographic settings [36,37], spin chains [21,22,[38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54], disordered systems [55][56][57][58] and for non-trivial topological phases [59][60][61].…”

Monodromy methods for torus conformal blocks and entanglement entropy at large central charge

“…In particular, the monodromy methods found in this paper may prove useful in deriving recursion relations in the dimensions of the exchanged operators for torus conformal blocks with better convergence properties than the known recursion relations in the central charge found in [30]. Moreover, the monodromy methods also pave the way to the study of other information theoretic quantities closely connected to the entanglement entropy such as entanglement negativity [35][36][37], symmetry resolved entanglement [38][39][40][41][42] or entwinement [43][44][45][46][47] for finite temperature states, providing opportunities for new insights into the physics of the dual AdS black holes. We hope to be able to report on further results in this direction in the future.…”

Comments on the holographic description of Narain theories

“…The microscopic description by itself will likely be insufficient: it will presumably depend on the metric G and B-field parameterizing Narain moduli space, but evaluating, for example, the spectral gap ∆ 1 (G, B) for given G and B would likely be as complicated on the bulk side as it is in the boundary theory. A crucial new ingredient necessary on the bulk side would be an analog of the Bekenstein-Hawking entropy formula for gauge fields [31,32], obtained potentially via embedding gauge theory into bona fide gravity in AdS 3 [33]. Presumably, if this formula were applied to the "BTZ" JHEP10(2021)197 configuration discussed in section 3 it would yield the Cardy formula (1.4), mirroring the conventional analysis for Virasoro theories and establishing the validity of (4.1).…”