Correlation Functions in $\text{T}\bar{\text{T}}$-deformed Theories on the Torus

Abstract

We study the correlation functions of local operators in unitary $\text{T}\bar{\text{T}}$-deformed field theories defined on a torus, using their formulation in terms of Jackiw-Teitelboim gravity. We focus on the two-point correlation function in momentum space when the undeformed theory is a conformal field theory. The large momentum behavior of the correlation function is computed and compared to that of $\text{T}\bar{\text{T}}$-deformed field theories defined on a plane. For the latter, the behavior found was ${\left(\frac{\sqrt{t}|q|}{\pi e}\right)}^{-\frac{t{q}^2}{\pi }}$, where $q$ is the momentum and $t$ is the deformation parameter. For a torus, the same behavior is found for $|q|<<L/t$, where $L$ is the torus' length scale. However, for $|q|>>L/t$, a different behavior is found: ${\left(\frac{2{\sqrt{t}}^5{q}^2}{\pi e{L}^3|T{|}^2}\right)}^{\frac{t{q}^2}{\pi }}$, where $T$ is the modular parameter of the torus. Hence, at large momentum, the correlator decays and then grows. This behavior suggests that operators carrying momentum $q$ are smeared on a distance scale $t|q|$. The difference from the plane's result illustrates the non-locality of the theory and the UV-IR mixing.

v1:25 pages + appendices, 7 figures. v2: slight modifications. v3: 31 pages + appendices, 8 figures. Final section added with a summary and discussion, and other slight modifications

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• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
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