Abstract
We show the \( T\overline{T} \) deformation of two-dimensional quantum field theories is equivalent to replacing the spacetime dependence of the fields with dependence on the indices of infinitely large matrices. We show how this correspondence explains the CDD phase dressing of the S-matrix and the general formula for the deformation of arbitrary correlation functions. We also describe how the Moyal deformation of self-dual gravity is a \( T\overline{T} \) deformation of the theory described by the Chalmers-Siegel action, where the \( T\overline{T} \) deformation is defined on the two-dimensional plane of interactions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
J. Cardy, The \( T\overline{T} \) deformation of quantum field theory as random geometry, JHEP 10 (2018) 186 [arXiv:1801.06895] [INSPIRE].
S. Dubovsky, V. Gorbenko and M. Mirbabayi, Asymptotic fragility, near AdS2 holography and \( T\overline{T} \), JHEP 09 (2017) 136 [arXiv:1706.06604] [INSPIRE].
S. Dubovsky, V. Gorbenko and G. Hernández-Chifflet, \( T\overline{T} \) partition function from topological gravity, JHEP 09 (2018) 158 [arXiv:1805.07386] [INSPIRE].
A.J. Tolley, \( T\overline{T} \) deformations, massive gravity and non-critical strings, JHEP 06 (2020) 050 [arXiv:1911.06142] [INSPIRE].
L. Freidel, Reconstructing AdS/CFT, arXiv:0804.0632 [INSPIRE].
E.A. Mazenc, V. Shyam and R.M. Soni, A \( T\overline{T} \) Deformation for Curved Spacetimes from 3d Gravity, arXiv:1912.09179 [INSPIRE].
R. Conti, S. Negro and R. Tateo, The \( T\overline{T} \) perturbation and its geometric interpretation, JHEP 02 (2019) 085 [arXiv:1809.09593] [INSPIRE].
J. Cardy and B. Doyon, \( T\overline{T} \) deformations and the width of fundamental particles, JHEP 04 (2022) 136 [arXiv:2010.15733] [INSPIRE].
J. Cardy, \( T\overline{T} \)-deformed modular forms, Commun. Num. Theor. Phys. 16 (2022) 435 [arXiv:2201.00478] [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].
G. Lechner, Construction of Quantum Field Theories with Factorizing S-Matrices, Commun. Math. Phys. 277 (2008) 821 [math-ph/0601022] [INSPIRE].
H. Grosse and G. Lechner, Noncommutative Deformations of Wightman Quantum Field Theories, JHEP 09 (2008) 131 [arXiv:0808.3459] [INSPIRE].
D. Buchholz, G. Lechner and S.J. Summers, Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories, Commun. Math. Phys. 304 (2011) 95 [arXiv:1005.2656] [INSPIRE].
G. Lechner, Deformations of QFTs and construction of models, in TT and Other Solvable Deformations of Quantum Field Theories at the Simons Centre for Goemetry and Physics, 2019, https://scgp.stonybrook.edu/video_portal/video.php?id=4026.
C.K. Zachos, D.B. Fairlie and T.L. Curtright, Quantum Mechanics in Phase Space, World Scientific (2017).
A. Banburski et al., Non-local Field Theory from Matrix Models, arXiv:2206.13458 [INSPIRE].
S. Frolov, \( T\overline{T} \) Deformation and the Light-Cone Gauge, Proc. Steklov Inst. Math. 309 (2020) 107 [arXiv:1905.07946] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Solving the Simplest Theory of Quantum Gravity, JHEP 09 (2012) 133 [arXiv:1205.6805] [INSPIRE].
J. Cardy, \( T\overline{T} \) deformation of correlation functions, JHEP 12 (2019) 160 [arXiv:1907.03394] [INSPIRE].
J. Kruthoff and O. Parrikar, On the flow of states under \( T\overline{T} \), arXiv:2006.03054 [INSPIRE].
G. Chalmers and W. Siegel, The selfdual sector of QCD amplitudes, Phys. Rev. D 54 (1996) 7628 [hep-th/9606061] [INSPIRE].
L. Smolin, The GNewton to 0 limit of Euclidean quantum gravity, Class. Quant. Grav. 9 (1992) 883 [hep-th/9202076] [INSPIRE].
R. Bittleston, A. Sharma and D. Skinner, Quantizing the non-linear graviton, arXiv:2208.12701 [INSPIRE].
J.F. Plebanski, Some solutions of complex Einstein equations, J. Math. Phys. 16 (1975) 2395 [INSPIRE].
R. Monteiro, Celestial chiral algebras, colour-kinematics duality and integrability, JHEP 01 (2023) 092 [arXiv:2208.11179] [INSPIRE].
W. Bu, S. Heuveline and D. Skinner, Moyal deformations, W1+∞ and celestial holography, JHEP 12 (2022) 011 [arXiv:2208.13750] [INSPIRE].
Y. Yargic, J. Lanier, L. Smolin and D. Wecker, A Cubic Matrix Action for the Standard Model and Beyond, arXiv:2201.04183 [INSPIRE].
G. Bonelli, N. Doroud and M. Zhu, \( T\overline{T} \)-deformations in closed form, JHEP 06 (2018) 149 [arXiv:1804.10967] [INSPIRE].
S. Chakrabarti and M. Raman, Chiral Decoupling from Irrelevant Deformations, JHEP 04 (2020) 190 [arXiv:2001.06870] [INSPIRE].
P. Caputa et al., Geometrizing \( T\overline{T} \), JHEP 03 (2021) 140 [Erratum ibid. 09 (2022) 110] [arXiv:2011.04664] [INSPIRE].
M. Guica and R. Monten, \( T\overline{T} \) and the mirage of a bulk cutoff, SciPost Phys. 10 (2021) 024 [arXiv:1906.11251] [INSPIRE].
E.A. Coleman, J. Aguilera-Damia, D.Z. Freedman and R.M. Soni, \( T\overline{T} \)-deformed actions and (1, 1) supersymmetry, JHEP 10 (2019) 080 [arXiv:1906.05439] [INSPIRE].
P. Caputa, J. Kruthoff and O. Parrikar, Building Tensor Networks for Holographic States, JHEP 05 (2021) 009 [Erratum ibid. 09 (2022) 112] [arXiv:2012.05247] [INSPIRE].
S. Datta and Y. Jiang, \( T\overline{T} \) deformed partition functions, JHEP 08 (2018) 106 [arXiv:1806.07426] [INSPIRE].
O. Aharony et al., Modular invariance and uniqueness of \( T\overline{T} \) deformed CFT, JHEP 01 (2019) 086 [arXiv:1808.02492] [INSPIRE].
V. Gorbenko, E. Silverstein and G. Torroba, dS/dS and \( T\overline{T} \), JHEP 03 (2019) 085 [arXiv:1811.07965] [INSPIRE].
A. Lewkowycz, J. Liu, E. Silverstein and G. Torroba, \( T\overline{T} \) and EE, with implications for (A)dS subregion encodings, JHEP 04 (2020) 152 [arXiv:1909.13808] [INSPIRE].
E. Coleman et al., De Sitter microstates from \( T\overline{T} \) + Λ2 and the Hawking-Page transition, JHEP 07 (2022) 140 [arXiv:2110.14670] [INSPIRE].
V. Shyam, \( T\overline{T} \) + Λ2 Deformed CFT on the Stretched dS3 Horizon, JHEP 04 (2022) 052 [arXiv:2106.10227] [INSPIRE].
M. Guica, An integrable Lorentz-breaking deformation of two-dimensional CFTs, SciPost Phys. 5 (2018) 048 [arXiv:1710.08415] [INSPIRE].
J. Aguilera-Damia et al., A path integral realization of joint \( J\overline{T} \), \( T\overline{J} \) and \( T\overline{T} \) flows, JHEP 07 (2020) 085 [arXiv:1910.06675] [INSPIRE].
A. Guevara, Towards Gravity From a Color Symmetry, arXiv:2209.00696 [INSPIRE].
Acknowledgments
Microsoft supported this research both by funding researchers and providing computational, logistical and other general resources.
We are grateful to Jaron Lanier and Kevin Scott of Microsoft in particular for support of this project. We also thank Lee Smolin for discussions.
V.S. is supported by the Branco Weiss Fellowship – Society in Science, administered by the ETH Zurich.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2209.11753
Rights and permissions
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.
About this article
Cite this article
Shyam, V., Yargic, Y. \( T\overline{T} \) deformed scattering happens within matrices. J. High Energ. Phys. 2023, 132 (2023). https://doi.org/10.1007/JHEP04(2023)132
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2023)132