A new spin on entanglement entropy

TL;DR

This paper extends the concepts of entanglement and thermodynamic entropy to higher spin theories, providing new formulas and demonstrating their consistency with conformal field theory calculations and gravitational field equations.

Contribution

It introduces higher spin extensions of the Wald and Ryu-Takayanagi formulas and connects entanglement entropy variations to linearized higher spin field equations.

Findings

Higher spin entanglement entropy formulas derived and studied.

Matching bulk higher spin results with CFT correlators involving higher spin charges.

First law of entanglement entropy implies linearized higher spin field equations.

Abstract

We argue that the usual notions of thermodynamic and entanglement entropy have novel analogs in the context of higher spin theories. In particular, the Wald and Ryu-Takayanagi formulas have natural higher spin extensions that we work out and study. On the CFT side, just as standard entanglement entropy in CFT_2 can be computed from twist field correlators, we demonstrate that by introducing corresponding operators carrying higher spin charge we can precisely reproduce our results from the bulk. We also show that the first law for entanglement entropy implies the linearized field equations for the metric and higher spin fields, generalizing recent work on deriving the linearized Einstein equations from the first law.