A further support for the statement that the action of the HRT-area generates a kink transformation in the pure AdS$_3$ gravity

TL;DR

This paper provides additional evidence that the HRT-area action induces a kink transformation in pure AdS$_3$ gravity by computing the boundary stress tensor bracket, confirming previous results through an alternative method.

Contribution

It offers a new computation of the boundary stress tensor bracket under the kink transformation, supporting the link between HRT-area action and kink transformations in AdS$_3$ gravity.

Findings

Reproduces previous results using a different approach

Confirms the role of HRT-area in generating kink transformations

Provides a detailed boundary stress tensor analysis

Abstract

It is stated that the action of the Hubeny-Rangamani-Takayanagi (HRT) area, which is viewed as an observable, generates a kink transformation in gravity. In this paper, we provide a further support for the kink transformation statement by performing a relevant computation. Specifically, by acting the kink transformation to the boundary stress tensor, we compute the bracket between the HRT area with the boundary stress tensor. Here we represent the boundary stress tensor in terms of initial data on the Cauchy surface under holographic renormalization. Our computation reproduces the same result as the one in arXiv:2203.04270 derived from a different approach.