The surface/state correspondence suggests that the bulk codimensional two surface could be dual to the quantum state in the holographic conformal field theory (CFT). Inspired by the cutoff-anti–de Sitter (AdS)/$T\overline{T}$-deformed-CFT correspondence, we propose that the quantum states of the two-dimensional $T\overline{T}$-deformed holographic CFT are dual to some particular surfaces in the ${\mathrm{AdS}}_3$ gravity. In particular, the time slice of the cutoff surface is dual to the ground state of the $T\overline{T}$-deformed CFT. We examine our proposal by studying the entanglement entropy and complexity. 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.

• Received 6 August 2019
• Accepted 17 April 2020

DOI:https://doi.org/10.1103/PhysRevD.101.106011

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Published by the American Physical Society