Wilson Lines and Entanglement Entropy in Higher Spin Gravity

TL;DR

This paper proposes a Wilson line-based method to compute holographic entanglement entropy in higher spin gravity theories, extending the Ryu-Takayanagi prescription to gauge-invariant formulations in AdS3.

Contribution

It introduces a gauge-invariant Wilson line approach for entanglement entropy in higher spin gravity, generalizing existing methods and demonstrating consistency with known results in spin-3 cases.

Findings

Recover many expected results for spin-3 gravity

Compute black hole entropies with higher spin charge

Align with previous literature on higher spin entanglement entropy

Abstract

Holographic entanglement entropy provides a direct connection between classical geometry and quantum entanglement; however the usual prescription does not apply to theories of higher spin gravity, where standard notions of geometry are no longer gauge invariant. We present a proposal for the holographic computation of entanglement entropy in field theories dual to higher spin theories of gravity in AdS3. These theories have a Chern-Simons description, and our proposal involves a Wilson line in an infinite-dimensional representation of the bulk gauge group. In the case of spin-2 gravity such Wilson lines are the natural coupling of a heavy point particle to gravity and so are equivalent to the usual prescription of Ryu and Takayanagi. For higher spin gravity they provide a natural generalization of these ideas. We work out spin-3 gravity in detail, showing that our proposal recovers many expected results and computes thermal entropies of black holes with higher spin charge, finding agreement with previous expressions in the literature. We encounter some peculiarities in the case of non-unitary RG flow backgrounds and outline future generalizations.