$$ T\overline{T} $$ deformations in curved space from 4D Chern-Simons theory

Py, Victor

doi:10.1007/jhep08(2022)101

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D S L(2 ) Gravitational Chern-simons1

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“…9 The 3d Chern-Simons theory can itself be viewed as the dimensional reduction of a 4d version of Chern-Simons. An interesting connection between 4d Chern-Simons and T T was discussed in [93].…”

Section: D S L(2 ) Gravitational Chern-simonsmentioning

confidence: 99%

$T\bar{T}$ in JT Gravity and BF Gauge Theory

et al. 2022

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JT gravity has a first-order formulation as a two-dimensional BF theory, which can be viewed as the dimensional reduction of the Chern-Simons description of 3d3d gravity. We consider {T\overbar{T}}TT¯-type deformations of the (0+1)(0+1)-dimensional dual to this 2d2d BF theory and interpret the deformation as a modification of the BF theory boundary conditions. The fundamental observables in this deformed BF theory, and in its 3d3d Chern-Simons lift, are Wilson lines and loops. In the 3d3d Chern-Simons setting, we study modifications to correlators involving boundary-anchored Wilson lines which are induced by a {T\overbar{T}}TT¯ deformation on the 2d2d boundary; results are presented at both the classical level (using modified boundary conditions) and the quantum-mechanical level (using conformal perturbation theory). Finally, we calculate the analogous deformed Wilson line correlators in 2d2d BF theory below the Hagedorn temperature where the principal series dominates over the discrete series.

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Section: D S L(2 ) Gravitational Chern-simonsmentioning

confidence: 99%