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

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.

arXiv comment21 pages + appendices, 1 figure. Few references added in v2

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Cited by in corpus (10)

• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• Quantum chaos, scrambling and operator growth in $T\bar{T}$ deformed SYK models
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Nonperturbative effects and resurgence in JT gravity at finite cutoff
• $T\bar{T}$-flow effects on torus partition functions
• Quantization of the ModMax Oscillator
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• $T\bar{T}$ deformation of random matrices
• Deforming the ODE/IM correspondence with $\mathrm{T}\bar{\mathrm{T}}$
• Aspects of $T\bar{T}+J\bar{T}$ deformed Schwarzian: From gravity partition function to late-time spectral form factor