Modular covariance and uniqueness of $J\bar{T}$ deformed CFTs

Abstract

We study families of two dimensional quantum field theories, labeled by a dimensionful parameter $\mu$, that contain a holomorphic conserved $U(1)$ current $J(z)$. We assume that these theories can be consistently defined on a torus, so their partition sum, with a chemical potential for the charge that couples to $J$, is modular covariant. We further require that in these theories, the energy of a state at finite $\mu$ is a function only of $\mu$, and of the energy, momentum and charge of the corresponding state at $\mu =0$, where the theory becomes conformal. We show that under these conditions, the torus partition sum of the theory at $\mu =0$ uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in $\mu$, to be that of a $\mu J\bar{T}$ deformed conformal field theory (CFT). We derive a flow equation for the $J\bar{T}$ deformed partition sum, and use it to study non-perturbative effects. We find non-perturbative ambiguities for any non-zero value of $\mu$, and comment on their possible relations to holography.

Minor corrections, comments added

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Cited by in corpus (32)

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• de Sitter Microstates from $T\bar{T}+{\Lambda }_2$ and the Hawking-Page Transition
• Correlation functions, entanglement and chaos in the $T\bar{T}$/$J\bar{T}$-deformed CFTs
• Conserved currents and $\text{T}{\bar{\text{T}}}_s$ irrelevant deformations of 2D integrable field theories
• TsT, $T\bar{T}$ and black strings
• Holographic integration of $T\bar{T}$ and $J\bar{T}$ via $O(d,d)$
• Entanglement and Rényi Entropy of Multiple Intervals in $T\overline{T}$-Deformed CFT and Holography
• On correlation functions in $J\bar{T}$-deformed CFTs
• $T\bar{T},J\bar{T}$, $T\bar{J}$ Partition Sums From String Theory
• Expectation value of $\mathrm{T}\overline{\mathrm{T}}$ operator in curved spacetimes
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• $T\bar{T}$, the entanglement wedge cross section, and the breakdown of the split property
• Boundary conditions for General Relativity in three-dimensional spacetimes, integrable systems and the KdV/mKdV hierarchies
• Heating up holography for single-trace $J\bar{T}$ deformations
• Geometrizing non-relativistic bilinear deformations
• Supersymmetric $J\bar{T}$ and $T\bar{J}$ deformations
• TsT, black holes, and $T\bar{T}+J\bar{T}+T\bar{J}$
• Very Special $T\bar{J}$ deformed CFT
• A Path Integral Realization of Joint $J\bar{T}$, $T\bar{J}$ and $T\bar{T}$ Flows
• A general definition of $J{T}_a$ -- deformed QFTs
• $T\bar{T}/J\bar{T}$-deformed WZW models from Chern-Simons AdS${}_3$ gravity with mixed boundary conditions
• Thermodynamics of $T\bar{T}$, $J\bar{T}$, $T\bar{J}$ deformed conformal field theories
• States, symmetries and correlators of $T\bar{T}$ and $J\bar{T}$ symmetric orbifolds
• Holographic Dual of Conformal Field Theories with Very Special $T\bar{J}$ Deformations
• Holographic entanglement entropy and mutual information in deformed field theories at finite temperature
• Current-current deformations, conformal integrals and correlation functions
• Supersymmetric black holes and $T\bar{T}$ deformation
• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
• Mixed state entanglement in deformed field theory at finite temperature