Correlation functions of CFTs on a torus with a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi><mml:mover accent="true"><mml:mi>T</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math> deformation
Song He, Yuan Sun
Abstract
In this paper, we investigate the correlation functions of the conformal field theory (CFT) with the $T\overline{T}$ deformation on a torus in terms of the perturbative CFT approach, which is the extension of the previous investigations on correlation functions defined on a plane. We systematically obtain the first-order correction to the correlation functions of the CFTs with a $T\overline{T}$ deformation in both operator formalism and path integral language. As a consistency check, we compute the deformed partition function, namely, the zero-point correlation function, up to the first order, which is consistent with results in the literature. Moreover, we obtain a new recursion relation for correlation functions with multiple $T$'s and $\overline{T}$'s inserted in generic CFTs on a torus. Based on the recursion relations, we study some correlation functions of stress tensors up to the first order under $T\overline{T}$ deformation.