$T\bar{T}$-flow effects on torus partition functions

Abstract

In this paper, we investigate the partition functions of conformal field theories (CFTs) with the $T\bar{T}$ deformation on a torus in terms of the perturbative QFT approach. In Lagrangian path integral formalism, the first- and second-order deformations to the partition functions of 2D free bosons, free Dirac fermions, and free Majorana fermions on a torus are obtained. The corresponding Lagrangian counterterms in these theories are also discussed. The first two orders of the deformed partition functions and the first-order vacuum expectation value (VEV) of the first quantum KdV charge obtained by the perturbative QFT approach are consistent with results obtained by the Hamiltonian formalism in literature.

arXiv comment40 pages, 1 figure; v4: Match the published version in JHEP

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• Marginal $T\bar{T}$-Like Deformation and ModMax Theories in Two Dimensions
• Geometric formulation of generalized root-$T\bar{T}$ deformations
• Manifestly $SL(2,R)$ Duality-Symmetric Forms in ModMax Theory
• Holographic torus correlators of stress tensor in $Ad{S}_3/CF{T}_2$
• Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy
• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• Perturbative renormalization of the $T\bar{T}$-deformed free massive Dirac fermion
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• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
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• Geometric realization via irrelevant deformations induced by the stress-energy tensor
• Note on higher-point correlation functions of the $T\bar{T}$ or $J\bar{T}$ deformed CFTs
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge