Bulk entanglement entropy for photons and gravitons in AdS$_3$

TL;DR

This paper investigates quantum corrections to holographic entanglement entropy in AdS$_3$/CFT$_2$, focusing on bulk gauge fields and gravitons, revealing how bulk entanglement renormalizes the holographic central charge and matches CFT calculations.

Contribution

It provides the first detailed analysis of bulk entanglement entropy for topological gauge fields and gravitons in AdS$_3$, including explicit calculations and the interplay of edge modes.

Findings

Bulk entanglement entropy renormalizes the holographic central charge.

Explicit map to extended Hilbert space for edge excitations.

Perfect agreement between bulk and CFT calculations of entropy differences.

Abstract

We study quantum corrections to holographic entanglement entropy in AdS$_3$/CFT$_2$; these are given by the bulk entanglement entropy across the Ryu-Takayanagi surface for all fields in the effective gravitational theory. We consider bulk $U(1)$ gauge fields and gravitons, whose dynamics in AdS$_3$ are governed by Chern-Simons terms and are therefore topological. In this case the relevant Hilbert space is that of the edge excitations. A novelty of the holographic construction is that such modes live not only on the bulk entanglement cut but also on the AdS boundary. We describe the interplay of these excitations and provide an explicit map to the appropriate extended Hilbert space. We compute the bulk entanglement entropy for the CFT vacuum state and find that the effect of the bulk entanglement entropy is to renormalize the relation between the effective holographic central charge and Newton's constant. We also consider excited states obtained by acting with the $U(1)$ current on the vacuum, and compute the difference in bulk entanglement entropy between these states and the vacuum. We compute this UV-finite difference both in the bulk and in the CFT finding a perfect agreement.