Correlation functions of the CFTs on torus with $T\bar{T}$ deformation

Understand

In this paper, we investigate the correlation functions of the conformal field theory (CFT) with the $T\bar{T}$ deformation on torus in terms of 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 $T\bar{T}$ 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 literature.
• Moreover, we obtain a new recursion relation for correlation functions with multiple $T$'s and $\bar{T}$'s insertion in generic CFTs on torus.