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

TL;DR

The paper investigates the surface/state correspondence in the context of cutoff AdS/CFT via TTbar deformation (cAdS/dCFT). It proposes that TTbar-deformed CFT ground states are dual to specific bulk surfaces, with the cutoff-time slice corresponding to the ground state, and it validates this through entanglement entropy analyses and a detailed study of quantum information metrics and complexity. The results show consistency with generalized RT entanglement, cMERA-based complexity, and holographic CV/CA prescriptions, supporting the proposed duality. The work suggests a coherent picture where TTbar scales map to cMERA layers, offering a concrete path to understanding spacetime emergence from quantum information in holography and proposing future extensions to thermofield double states and BTZ geometries.

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.

Figures (4)

• Figure 1: A codimension two surface $\Sigma$ corresponds to a quantum state $|\Phi(\Sigma)\rangle$.
• Figure 2: Generalized Ryu-Takayanagi formula.
• Figure 3: Quantum state $|\Omega^{(\mu)}\rangle$ of $\mathcal{T}^{(\mu)}$ lives on $\mathcal{S}^{r_{c}}$.
• Figure 4: The WdW patch for the Poincare patch of $AdS_{3}$. We introduced a regularized surface $r=\epsilon$.