Abstract
We study the evolution of correlation functions of local fields in a two-dimensional quantum field theory under the \( \lambda T\overline{T} \) deformation, suitably regularized. We show that this may be viewed in terms of the evolution of each field, with a Dirac-like string being attached at each infinitesimal step. The deformation then acts as a derivation on the whole operator algebra, satisfying the Leibniz rule. We derive an explicit equation which allows for the analysis of UV divergences, which may be absorbed into a non-local field renormalization to give correlation functions which are UV finite to all orders, satisfying a (deformed) operator product expansion and a Callan-Symanzik equation. We solve this in the case of a deformed CFT, showing that the Fourier-transformed renormalized two-point functions behave as k2∆+2λk2, where ∆ is their IR conformal dimension. We discuss in detail deformed Noether currents, including the energy-momentum tensor, and show that, although they also become non-local, when suitably improved they remain finite, conserved and satisfy the expected Ward identities. Finally, we discuss how the equivalence of the \( T\overline{T} \) deformation to a state-dependent coordinate transformation emerges in this picture.
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ArXiv ePrint: 1907.03394
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Cardy, J. \( T\overline{T} \) deformation of correlation functions. J. High Energ. Phys. 2019, 160 (2019). https://doi.org/10.1007/JHEP12(2019)160
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DOI: https://doi.org/10.1007/JHEP12(2019)160