Surface growth scheme for bulk reconstruction and $T\bar T$ deformation

TL;DR

This paper explores how the $T\bar{T}$ deformation in conformal field theory relates to surface growth in AdS spacetime, offering insights into bulk reconstruction and gravitational dynamics.

Contribution

It establishes a connection between surface growth schemes and $T\bar{T}$ deformation using tensor networks, providing a new dynamical perspective on bulk reconstruction.

Findings

Surface growth maps to $T\bar{T}$ operator flow.

Deformation drives the radial evolution of minimal surfaces.

Results suggest a mechanism for bulk gravitational dynamics reconstruction.

Abstract

In this paper, we study the dynamical connection between the surface growth scheme and the conformal field theory with $T\bar{T}$ deformation. By utilizing the extended one-shot entanglement distillation tensor network, we find that the iterative growth, i.e. radial evolution of homogenous and isotropic bulk minimal surfaces in asymptotically anti-de Sitter (AdS) spacetime can be mapped to the $T\bar{T}$ operator flow driven by the deformation parameter. Our results show that the $T\bar{T}$ deformation can provide a dynamical mechanism for the surface growth in asymptotically AdS spacetime, which may shed light on reconstructing bulk gravitational dynamics from the surface growth scheme.