Entanglement Entropy and Higher Spin Holography in AdS$_3$

TL;DR

This paper proposes a holographic method to compute entanglement entropy in higher spin AdS_3/CFT_2 dualities using Wilson lines in Chern-Simons theory, extending the standard Ryu-Takayanagi prescription.

Contribution

It introduces a Wilson line functional in Chern-Simons theory that captures entanglement entropy for higher spin holography, generalizing existing methods for standard AdS_3 gravity.

Findings

The Wilson line functional reproduces expected entanglement entropy features.

It obeys strong subadditivity in tested cases.

Reduces to thermal entropy in the high-temperature limit.

Abstract

A holographic correspondence has been recently developed between higher spin theories in three-dimensional anti-de Sitter space (AdS_3) and two-dimensional Conformal Field Theories (CFTs) with extended symmetries. A class of such dualities involves SL(N,R)\times SL(N,R) Chern-Simons gauge theories in the (2+1)-dimensional bulk spacetime, and CFTs with W_N symmetry algebras on the (1+1)-dimensional boundary. The topological character of the Chern-Simons theory forces one to reconsider standard geometric notions such as black hole horizons and entropy, as well as the usual holographic dictionary. Motivated by this challenge, in this note we present a proposal to compute entanglement entropy in the W_N CFTs via holographic methods. In particular, we introduce a functional constructed from Wilson lines in the bulk Chern-Simons theory that captures the entanglement entropy in the CFTs dual to standard AdS_3 gravity, corresponding to SL(2,R)\times SL(2,R) gauge group, and admits an immediate generalization to the higher spin case. We explicitly evaluate this functional for several known solutions of the Chern-Simons theory, including charged black holes dual to thermal CFT states carrying higher spin charge, and show that it reproduces expected features of entanglement entropy, study whether it obeys strong subadditivity, and moreover show that it reduces to the thermal entropy in the appropriate limit.