Abstract
In this paper, we investigate the partition functions of conformal field theories (CFTs) with the T\( \overline{T} \) deformation on a torus in terms of the perturbative QFT approach. In Lagrangian path integral formalism, the first- and second-order deformations to the partition functions of 2D free bosons, free Dirac fermions, and free Majorana fermions on a torus are obtained. The corresponding Lagrangian counterterms in these theories are also discussed. The first two orders of the deformed partition functions and the first-order vacuum expectation value (VEV) of the first quantum KdV charge obtained by the perturbative QFT approach are consistent with results obtained by the Hamiltonian formalism in literature.
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He, S., Sun, Y. & Zhang, YX. T \( \overline{T} \)-flow effects on torus partition functions. J. High Energ. Phys. 2021, 61 (2021). https://doi.org/10.1007/JHEP09(2021)061
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DOI: https://doi.org/10.1007/JHEP09(2021)061