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arXiv · 2012.03972

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

Shinji Hirano·Tatsuki Nakajima·Masaki Shigemori
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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.

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Shinji Hirano, Tatsuki Nakajima, Masaki Shigemori. 2020-12-07. $T\bar{T}$ Deformation of Stress-Tensor Correlators from Random Geometry. https://doi.org/10.1007/jhep04(2021)270

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