Abstract
We study the correlation functions of local operators in unitary \( \textrm{T}\overline{\textrm{T}} \)-deformed field theories, using their formulation in terms of Jackiw-Teitelboim gravity. The position of the operators is defined using the dynamical coordinates of this formalism. We focus on the two-point correlation function in momentum space, when the undeformed theory is a conformal field theory. In particular, we compute the large momentum behavior of the correlation functions, which manifests the non-locality of the \( \textrm{T}\overline{\textrm{T}} \)-deformed theory. The correlation function has UV-divergences, which are regulated by a point-splitting regulator. Renormalizing the operators requires multiplicative factors depending on the momentum, unlike the behavior in local QFTs. The large momentum limit of the correlator, which is the main result of this paper, is proportional to \( {\left|q\right|}^{-\frac{q^2}{\pi \left|\Lambda \right|}} \), where q is the momentum and 1/|Λ| is the deformation parameter. Interestingly, the exponent here has a different sign from earlier results obtained by resummation of small q computations. The decay at large momentum implies that the operators behave non-locally at the scale set by the deformation parameter.
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Acknowledgments
We would like to thank Sergei Dubovsky, Guzmán Hernández-Chifflet, Zohar Komargodski, David Kutasov, Onkar Parrikar, and Adar Sharon for useful discussions. This work was supported in part by an Israel Science Foundation (ISF) center for excellence grant (grant number 2289/18), by ISF grant no. 2159/22, by Simons Foundation grant 994296 (Simons Collaboration on Confinement and QCD Strings), by grant no. 2018068 from the United States-Israel Binational Science Foundation (BSF), by the Minerva foundation with funding from the Federal German Ministry for Education and Research, by the German Research Foundation through a German-Israeli Project Cooperation (DIP) grant “Holography and the Swampland”, and by a research grant from Martin Eisenstein. OA is the Samuel Sebba Professorial Chair of Pure and Applied Physics.
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Aharony, O., Barel, N. Correlation functions in \( \textrm{T}\overline{\textrm{T}} \)-deformed Conformal Field Theories. J. High Energ. Phys. 2023, 35 (2023). https://doi.org/10.1007/JHEP08(2023)035
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DOI: https://doi.org/10.1007/JHEP08(2023)035