Abstract
We consider the problem of exact integration of the \( T\overline{T} \) -deformation of two dimensional quantum field theories, as well as some higher dimensional extensions in the form of det T -deformations. When the action can be shown to only depend algebraically on the background metric the solution of the deformation equation on the Lagrangian can be given in closed form in terms of solutions of the (extended) Burgers’ equation. We present such examples in two and higher dimensions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K.G. Wilson, The renormalization group and critical phenomena, Rev. Mod. Phys. 55 (1983) 583 [INSPIRE].
J. Polchinski, Renormalization and Effective Lagrangians, Nucl. Phys. B 231 (1984) 269 [INSPIRE].
E. Abdalla, M.B. Abdalla and D. Rothe, Non-perturbative methods in 2 dimensional quantum field theory, World Scientific (1991) [INSPIRE].
A.B. Zamolodchikov, Expectation value of composite field \( T\overline{T} \) in two-dimensional quantum field theory, hep-th/0401146 [INSPIRE].
V. Fateev, D. Fradkin, S.L. Lukyanov, A.B. Zamolodchikov and A.B. Zamolodchikov, Expectation values of descendent fields in the sine-Gordon model, Nucl. Phys. B 540 (1999) 587 [hep-th/9807236] [INSPIRE].
G. Delfino and G. Niccoli, Matrix elements of the operator \( T\overline{T} \) in integrable quantum field theory, Nucl. Phys. B 707 (2005) 381 [hep-th/0407142] [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].
S. Dubovsky, R. Flauger and V. Gorbenko, Solving the Simplest Theory of Quantum Gravity, JHEP 09 (2012) 133 [arXiv:1205.6805] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Evidence from Lattice Data for a New Particle on the Worldsheet of the QCD Flux Tube, Phys. Rev. Lett. 111 (2013) 062006 [arXiv:1301.2325] [INSPIRE].
G. Mussardo and P. Simon, Bosonic type S matrix, vacuum instability and CDD ambiguities, Nucl. Phys. B 578 (2000) 527 [hep-th/9903072] [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].
M. Guica, An integrable Lorentz-breaking deformation of two-dimensional CFTs, arXiv:1710.08415 [INSPIRE].
J. Cardy, The \( T\overline{T} \) deformation of quantum field theory as a stochastic process, arXiv:1801.06895 [INSPIRE].
M. Baggio and A. Sfondrini, Strings on NS-NS Backgrounds as Integrable Deformations, arXiv:1804.01998 [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].
M. Asrat, A. Giveon, N. Itzhaki and D. Kutasov, Holography Beyond AdS, arXiv:1711.02690 [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, \( T\overline{T} \) and LST, JHEP 07 (2017) 122 [arXiv:1701.05576] [INSPIRE].
A. Giveon, N. Itzhaki and D. Kutasov, A solvable irrelevant deformation of AdS 3 /CF T 2, JHEP 12 (2017) 155 [arXiv:1707.05800] [INSPIRE].
S. van Leuven, E. Verlinde and M. Visser, Towards non-AdS Holography via the Long String Phenomenon, arXiv:1801.02589 [INSPIRE].
V. Shyam, Background independent holographic dual to \( T\overline{T} \) deformed CFT with large central charge in 2 dimensions, JHEP 10 (2017) 108 [arXiv:1707.08118] [INSPIRE].
G. Giribet, \( T\overline{T} \) -deformations, AdS/CFT and correlation functions, JHEP 02 (2018) 114 [arXiv:1711.02716] [INSPIRE].
A. Bzowski and M. Guica, The holographic interpretation of \( J\overline{T} \) -deformed CFTs, arXiv:1803.09753 [INSPIRE].
W. Cottrell and A. Hashimoto, Comments on \( T\overline{T} \) double trace deformations and boundary conditions, arXiv:1801.09708 [INSPIRE].
O. Aharony and T. Vaknin, The TT* deformation at large central charge, arXiv:1803.00100 [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].
D. Bernard and B. Doyon, A hydrodynamic approach to non-equilibrium conformal field theories, J. Stat. Mech. 1603 (2016) 033104 [arXiv:1507.07474] [INSPIRE].
A.M. Polyakov, Gauge Fields and Strings, Contemp. Concepts Phys. 3 (1987) 1 [INSPIRE].
R. Tateo, CDD ambiguity and irrelevant deformations of 2D QFT, Igst2017, https://www.phys.ens.fr/~igst17/slides/Tateo.pdf.
S. Dubovsky, V. Gorbenko and M. Mirbabayi, Natural Tuning: Towards A Proof of Concept, JHEP 09 (2013) 045 [arXiv:1305.6939] [INSPIRE].
A.B. Zamolodchikov, From tricritical Ising to critical Ising by thermodynamic Bethe ansatz, Nucl. Phys. B 358 (1991) 524 [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: 1804.10967
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
Bonelli, G., Doroud, N. & Zhu, M. \( T\overline{T} \) -deformations in closed form. J. High Energ. Phys. 2018, 149 (2018). https://doi.org/10.1007/JHEP06(2018)149
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2018)149