Quantum corrections to finite radius holography and holographic entanglement entropy

TL;DR

This paper computes quantum corrections to holographic entanglement entropy in a finite-radius AdS/CFT setup, establishing a detailed dictionary between deformed CFTs and bulk gravity, and confirming the Ryu--Takayanagi formula with quantum effects.

Contribution

It provides the first explicit calculation of quantum corrections to holographic entanglement entropy in finite-radius AdS holography, connecting flow equations to the Wheeler-DeWitt equation.

Findings

Quantum corrections match the generalized Ryu--Takayanagi formula.

The entanglement entropy includes bulk length operator expectation and fluctuation entropy.

The conformal mode problem is addressed and resolved.

Abstract

We calculate quantum corrections to holographic entanglement entropy in the proposed duality between $T\bar{T}$-deformed holographic 2D CFTs and gravity in AdS$_{3}$ with a finite cutoff. We first establish the dictionary between the two theories by mapping the flow equation of the deformed CFT to the bulk Wheeler-DeWitt equation. The latter reduces to an ordinary differential equation for the sphere partition function, which we solve to find the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere. The entanglement entropy in the inverse central charge expansion yields the expectation value of the bulk length operator plus the entropy of length fluctuations, in accordance with the Ryu--Takayanagi formula and its generalization due to Faulkner, Lewkowycz, and Maldacena. Special attention is paid to the conformal mode problem and its resolution by a choice of contour for the gravitational path integral.