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

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.