Entanglement entropy from surface terms in general relativity

TL;DR

This paper demonstrates that surface terms in general relativity, specifically the Gibbons-Hawking-York term, can accurately reproduce entanglement entropy in holographic duals like the BTZ black hole, linking gravity surface terms to quantum entanglement.

Contribution

It shows that surface terms in general relativity encode entanglement entropy in holographic duals, providing a new geometric perspective on quantum entanglement in gravity.

Findings

Gibbons-Hawking-York term reproduces entanglement entropy in BTZ black hole

Surface terms in gravity capture quantum entanglement effects

Holographic entanglement entropy can be derived from surface contributions

Abstract

Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighbourhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1+1 dimensional CFTs at finite temperature whose gravity dual is the BTZ black hole, the Gibbons-Hawking-York term precisely reproduces the entanglement entropy which can be computed independently in the field theory.