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

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.

💡 Research Summary

**
The paper provides a concrete verification of the claim that the Hubeny‑Rangamani‑Takayanagi (HRT) area operator generates a “kink transformation” in pure three‑dimensional anti‑de Sitter (AdS₃) gravity. The authors adopt a canonical Hamiltonian framework, representing all observables in terms of initial data on a Cauchy (Cauchy) surface—specifically the induced metric σₐb and extrinsic curvature Kₐb.

First, the HRT area A_HRT