# Surface/State correspondence and $T\overline{T}$ deformation

## TL;DR

This paper explores the duality between $Tar{T}$-deformed 2D holographic CFT states and specific surfaces in AdS$_3$ gravity, analyzing entanglement entropy and complexity to support the surface/state correspondence.

## Contribution

It proposes a novel duality between $Tar{T}$-deformed CFT states and particular bulk surfaces, extending the surface/state correspondence to deformed holographic theories.

## Key findings

- Ground state complexity matches cMERA and holographic complexity.
- Entanglement entropy behavior aligns with the proposed duality.
- Time slice of cut-off surface corresponds to the deformed CFT ground state.

## Abstract

The surface/state correspondence suggests that the bulk co-dimensional two surface could be dual to the quantum state in the holographic conformal field theory(CFT). Inspired by the cutoff-AdS/$T\overline{T}$-deformed-CFT correspondence, we propose that the quantum states of two-dimensional $T\overline{T}$-deformed holographic CFT are dual to some particular surfaces in the AdS$_3$ gravity. In particular, the time slice of the cut-off surface is dual to the ground state of the $T\overline{T}$-deformed CFT. We examine our proposal by studying the entanglement entropy and quantum information metric. We find that the complexity of the ground state in the deformed theory is consistent with the one of a particular cMERA and the holographic complexity via CV or CA prescription.