A Path Integral Realization of Joint $J\bar{T}$, $T\bar{J}$ and $T\bar{T}$ Flows

Abstract

We recast the joint $J\bar{T}$, $T\bar{J}$ and $T\bar{T}$ deformations as coupling the original theory to a mixture of topological gravity and gauge theory. This geometrizes the general flow triggered by irrelevant deformations built out of conserved currents and the stress-energy tensor, by means of a path integral kernel. The partition function of the deformed theory satisfies a diffusion-like flow equation similar to that found in the pure $T\bar{T}$ case. Our proposal passes two stringent tests. Firstly, we recover the classical deformed actions from the kernel, reproducing the known expressions for the free boson and fermion. Secondly, we explicitly compute the torus path integral along the flow and show it localizes to a finite-dimensional, one-loop exact integral over base space torus moduli. The dressed energy levels so obtained match exactly onto those previously reported in the literature.

References in corpus (26)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Asymptotic Fragility, Near $Ad{S}_2$ Holography and $T\bar{T}$
• The $T\overline{T}$ deformation of quantum field theory as random geometry
• $T\bar{T}$ Partition Function from Topological Gravity
• An integrable Lorentz-breaking deformation of two-dimensional CFTs
• The $\text{T}\bar{\text{T}}$ perturbation and its geometric interpretation
• Modular invariance and uniqueness of $T\bar{T}$ deformed CFT
• Entanglement entropy and $T\overline{T}$ deformation
• Holography Beyond AdS
• A Solvable Irrelevant Deformation of $Ad{S}_3/CF{T}_2$
• $T\bar{T}$ and EE, with implications for (A)dS subregion encodings
• The holographic interpretation of $J\bar{T}$-deformed CFTs
• Entanglement Beyond $\mathrm{AdS}$
• $J\bar{T}$ deformed $CF{T}_2$ and String Theory
• Strings on warped AdS${}_3$ via $T\bar{J}$ deformations
• Conserved currents and $\text{T}{\bar{\text{T}}}_s$ irrelevant deformations of 2D integrable field theories
• Constraints on Flavored 2d CFT Partition Functions
• On correlation functions in $J\bar{T}$-deformed CFTs
• $T\bar{T}$-Deformed Actions and (1,1) Supersymmetry
• Modular covariance and uniqueness of $J\bar{T}$ deformed CFTs
• $T\bar{T},J\bar{T}$, $T\bar{J}$ Partition Sums From String Theory
• $T\overline{T}$, $\tilde{J}J$, $JT$ and $\tilde{J}T$ deformations
• Expectation value of $\mathrm{T}\overline{\mathrm{T}}$ operator in curved spacetimes
• Heating up holography for single-trace $J\bar{T}$ deformations
• Quantum corrections to finite radius holography and holographic entanglement entropy

Cited by in corpus (13)

• 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
• Geometrizing non-relativistic bilinear deformations
• $T\overline{T}$ deformation in SCFTs and integrable supersymmetric theories
• Topological Gauging and Double Current Deformations
• A general definition of $J{T}_a$ -- deformed QFTs
• $T\bar{T}$ and $J\bar{T}$ Deformations in Quantum Mechanics
• $T\bar{T}$ deformation on multiquantum mechanics and regenesis
• $T\bar{T}+{\Lambda }_2$ from a 2d gravity path integral
• Irrelevant Deformations with Boundaries and Defects
• Characters of irrelevant deformations
• Phase Transition in JT Gravity and $T\bar{T}$ Deformation
• $T\bar{T}$ deformed scattering happens within matrices