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Abstract

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,
and later generalize it to the higher order perturbations which are involved in
the multiple $T$ and $\bar{T}$ insertion. As consistenty checks, we compute the
deformed partition function, namely zero-point correlation function, up-to
leading order and check the results in the free field theories as examples.
Further, we also get the second order formula of the partition function which
is consistent with previous result in literature.