Generalized entropy of photons in AdS

TL;DR

This paper investigates quantum corrections to holographic entanglement entropy caused by photon excitations in AdS, demonstrating the vanishing contribution of electromagnetic edge modes and matching CFT and AdS calculations.

Contribution

It provides the first detailed holographic analysis of photon-induced quantum corrections to entanglement entropy, including the role of electromagnetic edge modes.

Findings

Electromagnetic edge modes do not contribute to the vacuum-subtracted von Neumann entropy.

Exact agreement between CFT entanglement entropy and AdS generalized entropy was achieved.

Photon excited states' quantum corrections are computed holographically in any dimension.

Abstract

This work analyzes the quantum corrections to holographic entanglement entropy at first subleading order in $G_{N}$ due to photon excited states in AdS. We compute the vacuum-subtracted von Neumann entropy of a $U(1)$ current excited state for a polar cap region on the cylinder in any large-$N$, strongly-coupled CFT$_{d}$ holographically dual to weakly-coupled Einstein gravity for any dimension $d>2$. We then quantize a Maxwell field in AdS$_{d+1}$ dual to the $U(1)$ current and consider a photon excited state whose vacuum-subtracted generalized entropy for the entanglement wedge is calculated. In order to factorise the Maxwell Hilbert space in AdS, we construct an extended Hilbert space and the corresponding electromagnetic edge modes. We find exact agreement between the CFT entanglement entropy and AdS generalized entropy without the inclusion of entropy of the edge modes. Finally, we show via explicit calculation that the contribution to the vacuum-subtracted von Neumann entropy from electromagnetic edge modes indeed vanishes, which is crucial for consistency with known holographic entropy formulas.