T T ¯ $$ \overline{T} $$ -flow effects on torus partition functions

• Main Authors: Song He, Yuan Sun, Yu-Xuan Zhang
• Format: Article
• Language: English
• Published: SpringerOpen 2021-09-01
• Series: Journal of High Energy Physics
• Subjects: Conformal Field Theory; Field Theories in Lower Dimensions; Integrable Field Theories; Renormalization Regularization and Renormalons
• Online Access: https://doi.org/10.1007/JHEP09(2021)061

Abstract In this paper, we investigate the partition functions of conformal field theories (CFTs) with the T 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.