$T\bar{T}$ Deformation of Stress-Tensor Correlators from Random Geometry

Abstract

We study stress-tensor correlators in the $T\bar{T}$-deformed conformal field theories in two dimensions. Using the random geometry approach to the $T\bar{T}$ deformation, we develop a geometrical method to compute stress-tensor correlators. More specifically, we derive the $T\bar{T}$ deformation to the Polyakov-Liouville conformal anomaly action and calculate three and four-point correlators to the first-order in the $T\bar{T}$ deformation from the deformed Polyakov-Liouville action. The results are checked against the standard conformal perturbation theory computation and we further check consistency with the $T\bar{T}$-deformed operator product expansions of the stress tensor. A salient feature of the $T\bar{T}$-deformed stress-tensor correlators is a logarithmic correction that is absent in two and three-point functions but starts appearing in a four-point function.

arXiv commentv2: JHEP version + minor corrections

References in corpus (16)

• The Holographic Weyl anomaly
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Asymptotic Fragility, Near $Ad{S}_2$ Holography and $T\bar{T}$
• Solving the Simplest Theory of Quantum Gravity
• Cutoff AdS${}_3$ versus the $T\bar{T}$ deformation
• The $T\overline{T}$ deformation of quantum field theory as random geometry
• $T\bar{T}$ Partition Function from Topological Gravity
• The $\text{T}\bar{\text{T}}$ perturbation and its geometric interpretation
• $T\bar{T}$ and the mirage of a bulk cutoff
• $T\bar{T}$ deformed CFT as a non-critical string
• Geometrizing $T\bar{T}$
• Random Boundary Geometry and Gravity Dual of $T\bar{T}$ Deformation
• $T\bar{T}$-deformation and Liouville gravity
• Large N Analysis of $T\bar{T}$-deformation and Unavoidable Negative-norm States

Cited by in corpus (10)

• 3D Gravity in a Box
• Field Theory of Interacting Boundary Gravitons
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Conformal Field Theories
• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• Aspects of $T\bar{T}+J\bar{T}$ deformed Schwarzian: From gravity partition function to late-time spectral form factor
• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
• $T\overline{T}$-deformed free energy of the Airy model
• Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Theories on the Torus
• Systematic approach to correlators in $T\bar{T}$ deformed CFTs
• Quantum deformation of cubic string field theory