$T\bar{T}$ deformation of correlation functions

Abstract

We study the evolution of correlation functions of local fields in a two-dimensional quantum field theory under the $\lambda T\bar{T}$ 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 $k^{2\Delta +2\lambda k^2}$, where $\Delta$ 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 $T\bar{T}$ deformation to a state-dependent coordinate transformation emerges in this picture.

25 pages, 2 figures. v2: version accepted for publication: absence of power law divergences clarified

References in corpus (7)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Solving the Simplest Theory of Quantum Gravity
• The $\text{T}\bar{\text{T}}$ perturbation and its geometric interpretation
• Conserved currents and $\text{T}{\bar{\text{T}}}_s$ irrelevant deformations of 2D integrable field theories
• Expectation value of composite field $T\bar{T}$ in two-dimensional quantum field theory
• $T\overline{T}$ deformations of non-Lorentz invariant field theories

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• Burgers Equation vs. Large $N$ Limit in $T\bar{T}$-deformed $O(N)$ Vector Model