Holographic entanglement entropy and gravitational anomalies

TL;DR

This paper explores how gravitational anomalies in 2D conformal field theories affect holographic entanglement entropy, revealing a ribbon-like minimal surface and linking it to spinning particles in 3D gravity.

Contribution

It introduces a novel holographic entanglement entropy functional accounting for gravitational anomalies, connecting it to spinning particles and their equations of motion.

Findings

Anomalies broaden the minimal surface into a ribbon.

Entanglement entropy relates to the twist of the ribbon.

Agreement with conformal field theory calculations.

Abstract

We study entanglement entropy in two-dimensional conformal field theories with a gravitational anomaly. In theories with gravity duals, this anomaly is holographically represented by a gravitational Chern-Simons term in the bulk action. We show that the anomaly broadens the Ryu-Takayanagi minimal worldline into a ribbon, and that the anomalous contribution to the CFT entanglement entropy is given by the twist in this ribbon. The entanglement functional may also be interpreted as the worldline action for a spinning particle -- that is, an anyon -- in three-dimensional curved spacetime. We demonstrate that the minimization of this action results in the Mathisson-Papapetrou-Dixon equations of motion for a spinning particle in three dimensions. We work out several simple examples and demonstrate agreement with CFT calculations.