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High Energy Physics - Theory, hep-th
Abstract:
In this paper, we investigate the partition functions of the conformal field
theories (CFTs) with the $T\bar{T}$ deformation on torus in terms of
perturbative QFT approach. In path integral formalism, the first and second
order deformations to the partition functions of the 2D free boson, free Dirac
fermion and free Majornana fermion on torus are obtained. In the free fermion,
we find that the first two orders of the deformed partition functions are
consistent with results obtained by the operator formalism. In the free boson,
the first order of the deformation to the partition function is the same as the
deformed partition function given by the operator formalism, however, the
second order correction to the partition function contains additional
contribution from the $T\bar{T}-$flow effect in the path integral formalism.
