$T\bar{T}$ and $J\bar{T}$ Deformations in Quantum Mechanics

TL;DR

This paper explores $Tar{T}$ and $Jar{T}$ deformations in quantum mechanics, deriving flow equations for partition functions, and proposes a non-perturbative UV completion via coupling to worldline gravity and gauge theory.

Contribution

It introduces analogues of $Jar{T}$ and mixed deformations in quantum mechanics, and develops a kernel-based method to analyze their effects on partition functions and correlators.

Findings

Derived flow equations for deformed partition functions.

Established kernel formulas for two-point functions.

Proposed a non-perturbative UV completion via coupling to gravity and gauge fields.

Abstract

In this paper, we continue the study of $T\bar{T}$ deformation in $d=1$ quantum mechanical systems and propose possible analogues of $J\bar{T}$ deformation and deformation by a general linear combination of $T\bar{T}$ and $J\bar{T}$ in quantum mechanics. We construct flow equations for the partition functions of the deformed theory, the solutions to which yields the deformed partition functions as integral of the undeformed partition function weighted by some kernels. The kernel formula turns out to be very useful in studying the deformed two-point functions and analyzing the thermodynamics of the deformed theory. Finally, we show that a non-perturbative UV completion of the deformed theory is given by minimally coupling the undeformed theory to worldline gravity and $U(1)$ gauge theory.