Entanglement Renormalization of a $T\bar{T}$-deformed CFT

TL;DR

This paper employs cMERA to analyze a $T\bar{T}$-deformed scalar CFT, revealing mild non-localities and insights into the holographic dual, including the implications for bulk geometry and entanglement.

Contribution

It provides a Gaussian approximation to the ground state of a $T\bar{T}$-deformed CFT using cMERA and explores the resulting entanglement and non-locality features.

Findings

Non-localities are mild and do not violate the area law.

A finite bulk radius can be defined in the holographic dual.

Entropy analysis challenges the absence of geometry outside the radial cutoff.

Abstract

In this work we use cMERA, a continuous tensor network, to find a Gaussian approximation to the ground state of a $T\bar{T}$-deformed scalar CFT on the line, to first order in the deformation parameter. The result is used to find the correction to the correlators of scaling operators of the theory and to the entanglement entropy of a half-line. From the latter, we discuss the non-localities induced by the $T\bar{T}$-deformation at short length scales. We find that the kind of non-locality generated by those terms can be considered as a mild-one, in the sense that it does not violate the area law of entanglement. In the context of the conjectured connection between cMERA and holography, we find that at first insight a finite bulk radius can be defined in the putative geometric dual description of cMERA. However, the entropy analysis contradicts the proposal that no geometry can be ascribed to the region outside this radial cutoff.