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

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.

7 pages, 4 figures

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Cited by in corpus (17)

• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• Quantum Information in Holographic Duality
• Correlation functions of the CFTs on torus with $T\bar{T}$ deformation
• The correlation function of (1,1) and (2,2) supersymmetric theories with $T\bar{T}$ deformation
• Cutoff Dependence and Complexity of the CFT${}_2$ Ground State
• Spacetime as a quantum circuit
• Note on the nonrelativistic $T\bar{T}$ deformation
• End of the World Brane meets $T\bar{T}$
• Surface growth scheme for bulk reconstruction and tensor network
• $T\bar{T}/J\bar{T}$-deformed WZW models from Chern-Simons AdS${}_3$ gravity with mixed boundary conditions
• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• Exploring causality in braneworld/cutoff holography via holographic scattering
• Non-equilibrium dynamics in Holography
• Note on higher-point correlation functions of the $T\bar{T}$ or $J\bar{T}$ deformed CFTs
• On the symmetry of $T\bar{T}$ deformed CFT
• Geometry of Entanglement
• Cost of holographic path integrals