Correlation functions of the CFTs on torus with $T\bar{T}$ deformation

Abstract

In this paper, we investigate the correlation functions of the conformal field theory (CFT) with the $T\bar{T}$ deformation on torus in terms of perturbative CFT approach, which is the extension of the previous investigations on correlation functions defined on a plane. We systematically obtain the first order correction to the correlation functions of the CFTs with $T\bar{T}$ deformation in both operator formalism and path integral language. As a consistency check, we compute the deformed partition function, namely the zero-point correlation function, up to the first order, which is consistent with results in literature. Moreover, we obtain a new recursion relation for correlation functions with multiple $T$'s and $\bar{T}$'s insertion in generic CFTs on torus. Base on the recursion relations, we study some correlation functions of stress tensors up to the first order under $T\bar{T}$ deformation.

37 pages, Major revision, focus on the first order correction

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Cited by in corpus (34)

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• Field Theory of Interacting Boundary Gravitons
• Marginal $T\bar{T}$-Like Deformation and ModMax Theories in Two Dimensions
• Cutoff $\mathrm{Ad}{\mathrm{S}}_3$ versus $\mathrm{T}\bar{\mathrm{T}}$ $\mathrm{CF}{\mathrm{T}}_2$ in the large central charge sector: correlators of energy-momentum tensor
• Manifestly $SL(2,R)$ Duality-Symmetric Forms in ModMax Theory
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Conformal Field Theories
• Geometrizing non-relativistic bilinear deformations
• $T\bar{T}$ deformation of chiral bosons and Chern-Simons AdS${}_3$ gravity
• Holographic torus correlators of stress tensor in $Ad{S}_3/CF{T}_2$
• $T\bar{T}$-flow effects on torus partition functions
• $T\bar{T}$ flow as characteristic flows
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• Holographic entanglement entropy in $T\overline{T}$-deformed AdS${}_3$
• Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy
• $T\bar{T}/J\bar{T}$-deformed WZW models from Chern-Simons AdS${}_3$ gravity with mixed boundary conditions
• $T\bar{T}$ deformation on multiquantum mechanics and regenesis
• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• Irrelevant Deformations of Chiral Bosons
• Perturbative renormalization of the $T\bar{T}$-deformed free massive Dirac fermion
• Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus
• $T\bar{T}$ deformed soft theorem
• Spatial regions, chaos bound and its violation
• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
• Supersymmetric black holes and $T\bar{T}$ deformation
• Aspects of $T\bar{T}+J\bar{T}$ deformed Schwarzian: From gravity partition function to late-time spectral form factor
• $T\overline{T}$-deformed free energy of the Airy model
• Mixed state entanglement in deformed field theory at finite temperature
• Asymptotic Symmetries in the TsT/$T\bar{T}$ Correspondence
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Theories on the Torus
• 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
• Loop corrections versus marginal deformation in celestial holography
• Nonperturbative aspects of two-dimensional $T\bar{T}$-deformed scalar theory from functional renormalization group