Holographic Entanglement Entropy for Gravitational Anomaly in Four Dimensions

TL;DR

This paper calculates holographic entanglement entropy in four-dimensional theories with gravitational anomalies, revealing a parity-odd contribution and a divergence linked to geometric perturbations.

Contribution

It introduces a perturbative method to compute entanglement entropy for gravitational anomalies in 4D holography, including parity-odd effects from Chern-Simons terms.

Findings

Parity-odd entanglement entropy contribution identified

Matching of bulk and boundary contributions at leading order

Logarithmic divergence interpreted as source ignorance

Abstract

We compute the holographic entanglement entropy for the anomaly polynomial $\mathrm{Tr} R^2$ in 3+1 dimensions. Using the perturbative method developed for computing entanglement entropy for quantum field theories, we also compute the parity odd contribution to the entanglement entropy of the dual field theory that comes from a background gravitational Chern-Simons term. We find that, in leading order in the perturbation of the background geometry, the two contributions match except for a logarithmic divergent term on the field theory side. We interpret this extra contribution as encoding our ignorance of the source which creates the perturbation of the geometry.