Entanglement entropy and $T \overline{T}$ deformation

TL;DR

This paper investigates how the $T ar{T}$ deformation in conformal field theories acts as an ultraviolet cutoff, affecting entanglement entropy and supporting the duality with finite-region quantum gravity.

Contribution

It provides a detailed analysis of entanglement entropy in $T ar{T}$-deformed CFTs, confirming the finite-region holographic duality conjecture through explicit calculations.

Findings

Entanglement entropy is finite and matches the Ryu-Takayanagi formula for finite regions.

A family of conical entropies are finite and verify Dong's conjecture.

The $T ar{T}$ deformation acts as an ultraviolet cutoff on entanglement entropy.

Abstract

Quantum gravity in a finite region of spacetime is conjectured to be dual to a conformal field theory deformed by the irrelevant operator $T \overline{T}$. We test this conjecture with entanglement entropy, which is sensitive to ultraviolet physics on the boundary while also probing the bulk geometry. We find that the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere is finite and precisely matches the Ryu-Takayanagi formula applied to a finite region consistent with the conjecture of McGough, Mezei and Verlinde. We also consider a one-parameter family of conical entropies, which are finite and verify a conjecture due to Dong. Since ultraviolet divergences are local, we conclude that the $T \overline{T}$ deformation acts as an ultraviolet cutoff on the entanglement entropy. Our results support the conjecture that the $T \overline{T}$-deformed CFT is the holographic dual of a finite region of spacetime.