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High Energy Physics - Theory

arXiv:1805.07386 (hep-th)
[Submitted on 18 May 2018 (v1), last revised 12 Nov 2018 (this version, v2)]

Title:$T\bar{T}$ Partition Function from Topological Gravity

Authors:Sergei Dubovsky, Victor Gorbenko, Guzman Hernandez-Chifflet
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Abstract:The $T{\bar T}$ deformation of a relativistic two-dimensional theory results in a solvable gravitational theory. Deformed scattering amplitudes can be obtained from coupling the undeformed theory to the flat space Jackiw--Teitelboim (JT) gravity. We show that the JT description is applicable and useful also in finite volume. Namely, we calculate the torus partition function of an arbitrary matter theory coupled to the JT gravity, formulated in the first order (vierbein) formalism. The first order description provides a natural set of dynamical clocks and rods for this theory, analogous to the target space coordinates in string theory. These dynamical coordinates play the role of relational observables allowing to define a torus path integral for the JT gravity. The resulting partition function is one-loop exact and reproduces the $T\bar{T}$ deformed finite volume spectrum.
Comments: 21 pages, 1 figure; v2: typos fixed and some notation clarified, as compared to the JHEP version
Subjects: High Energy Physics - Theory (hep-th)
Cite as: arXiv:1805.07386 [hep-th]
  (or arXiv:1805.07386v2 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.1805.07386
Related DOI: https://doi.org/10.1007/JHEP09%282018%29158

Submission history

From: Victor Gorbenko [view email]
[v1] Fri, 18 May 2018 18:36:43 UTC (111 KB)
[v2] Mon, 12 Nov 2018 15:16:41 UTC (112 KB)
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