Abstract
The \( T\overline{T} \) 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 (vielbein) 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 \( T\overline{T} \) deformed finite volume spectrum.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Dubovsky, V. Gorbenko and M. Mirbabayi, Natural Tuning: Towards A Proof of Concept, JHEP 09 (2013) 045 [arXiv:1305.6939] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Solving the Simplest Theory of Quantum Gravity, JHEP 09 (2012) 133 [arXiv:1205.6805] [INSPIRE].
M. Caselle, D. Fioravanti, F. Gliozzi and R. Tateo, Quantisation of the effective string with TBA, JHEP 07 (2013) 071 [arXiv:1305.1278] [INSPIRE].
F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].
A. Cavaglià, S. Negro, I. M. Szécsényi, and R. Tateo, \( T\overline{T} \) -deformed 2D Quantum Field Theories, JHEP 10 (2016) 112 [arXiv:1608.05534] [INSPIRE].
A.B. Zamolodchikov, Expectation value of composite field \( T\overline{T} \) in two-dimensional quantum field theory, hep-th/0401146 [INSPIRE].
J. Cardy, The \( T\overline{T} \) deformation of quantum field theory as random geometry, arXiv:1801.06895 [INSPIRE].
S. Dubovsky, V. Gorbenko and M. Mirbabayi, Asymptotic fragility, near AdS 2 holography and \( T\overline{T} \), JHEP 09 (2017) 136 [arXiv:1706.06604] [INSPIRE].
E. Witten, On the Structure of the Topological Phase of Two-dimensional Gravity, Nucl. Phys. B 340 (1990) 281 [INSPIRE].
E. Witten, Two-dimensional gravity and intersection theory on moduli space, Surveys Diff. Geom. 1 (1991) 243 [INSPIRE].
R. Dijkgraaf and E. Witten, Developments in Topological Gravity, arXiv:1804.03275 [INSPIRE].
S. Dubovsky and G. Hernandez-Chifflet, Yang-Mills Glueballs as Closed Bosonic Strings, JHEP 02 (2017) 022 [arXiv:1611.09796] [INSPIRE].
L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \( T\overline{T} \), JHEP 04 (2018) 010 [arXiv:1611.03470] [INSPIRE].
J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge University Press, Cambridge U.K. (1998).
J. Polchinski, Evaluation of the One Loop String Path Integral, Commun. Math. Phys. 104 (1986) 37 [INSPIRE].
M. Dodelson, E. Silverstein and G. Torroba, Varying dilaton as a tracer of classical string interactions, Phys. Rev. D 96 (2017) 066011 [arXiv:1704.02625] [INSPIRE].
J.J. Duistermaat and G.J. Heckman, On the Variation in the cohomology of the symplectic form of the reduced phase space, Invent. Math. 69 (1982) 259.
S. Dubovsky and V. Gorbenko, Towards a Theory of the QCD String, JHEP 02 (2016) 022 [arXiv:1511.01908] [INSPIRE].
S. Dubovsky, A Simple Worldsheet Black Hole, JHEP 07 (2018) 011 [arXiv:1803.00577] [INSPIRE].
A.M. Polyakov, Quantum Geometry of Bosonic Strings, Phys. Lett. B 103 (1981) 207 [INSPIRE].
M. Guica, An integrable Lorentz-breaking deformation of two-dimensional CFTs, arXiv:1710.08415 [INSPIRE].
A. Bzowski and M. Guica, The holographic interpretation of \( J\overline{T} \) -deformed CFTs, arXiv:1803.09753 [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, \( \mathrm{T}\overline{\mathrm{T}} \) and LST, JHEP 07 (2017) 122 [arXiv:1701.05576] [INSPIRE].
E. D’Hoker and D.H. Phong, The Geometry of String Perturbation Theory, Rev. Mod. Phys. 60 (1988) 917 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1805.07386
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Dubovsky, S., Gorbenko, V. & Hernández-Chifflet, G. \( T\overline{T} \) partition function from topological gravity. J. High Energ. Phys. 2018, 158 (2018). https://doi.org/10.1007/JHEP09(2018)158
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2018)158