$T\bar T$ deformation on multiquantum mechanics and regenesis

TL;DR

This paper explores the effects of $Tar T$ deformation on various quantum mechanical systems, revealing regenesis phenomena and their gravitational duals in $AdS_2/CFT_1$ correspondence.

Contribution

It introduces a dynamical coordinate transformation approach to $Tar T$ deformation in quantum mechanics and demonstrates regenesis phenomena across multiple models.

Findings

Regenesis phenomena observed in quantum systems under $Tar T$ deformation.

Boundary graviton exchange explains regenesis in $AdS_2$ gravity.

Consistent reformulation of $Tar T$ deformation with previous literature.

Abstract

We study the $T\bar T$ deformation on multiquantum mechanical systems. By introducing dynamical coordinate transformation, we reformulate the one-dimensional $T\bar T$ deformation of generic quantum mechanical systems, which is consistent with the previous proposal in the literature. We further study the thermo-field-double state under the $T\bar T$ deformation on these systems, which include the conformal quantum mechanical system, the Sachdev-Ye-Kitaev model, and the model satisfying eigenstate thermalization hypothesis. We find common regenesis phenomena in which the signal injected into one local system can regenerate from the other local system. From the $AdS_2/CFT_1$ perspective, we study the deformation of Jackiw-Teitelboim gravity governed by Schwarzian action and find that these regenesis phenomena are realized by exchanging boundaries graviton via the nonlocal $T\bar T$ coupling.