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.
Highlights
The study of the black hole thermodynamics inspired ’t Hooft and Susskind [1,2] to propose holography as the guiding principle of quantum gravity
Inspired by the cutoff-anti–de Sitter (AdS)/TT -deformed-conformal field theory (CFT) correspondence, we propose that the quantum states of the two-dimensional TT -deformed holographic CFT are dual to some particular surfaces in the AdS3 gravity
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
Summary
The study of the black hole thermodynamics inspired ’t Hooft and Susskind [1,2] to propose holography as the guiding principle of quantum gravity. As the boundary moves into the bulk, one gets a series of codimension-one hypersurfaces, whose codimension-two time slices are where the quantum states of the TT -deformed CFTs dwell. This fact inspires us to propose the surface/state correspondence in the cAdS/. If the quantum field theory is a holographic CFT, the cAdS/dCFT correspondence claims that the deformed theory T ðμÞ is dual to a gravitational theory living in a finite region in AdS3 with a radial cutoff at r 1⁄4 rc, where the metric can be written as ds.
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