Solving a family of $T\bar{T}$-like theories

Bruno Le Floch (1) , Márk Mezei

1 IPM - institut de Physique Théorique Philippe Meyer

We deform two-dimensional quantum field theories by antisymmetric combinations of their conserved currents that generalize Smirnov and Zamolodchikov's $T\bar{T}$ deformation. We obtain that energy levels on a circle obey a transport equation analogous to the Burgers equation found in the $T\bar{T}$ case. This equation relates charges at any value of the deformation parameter to charges in the presence of a (generalized) Wilson line. We determine the initial data and solve the transport equations for antisymmetric combinations of flavor symmetry currents and the stress tensor starting from conformal field theories. Among the theories we solve is a conformal field theory deformed by $J\bar{T}$ and $T\bar{T}$ simultaneously. We check our answer against results from AdS/CFT.

Mots clés: field theory: conformal; field theory: deformation; symmetry: flavor; tensor: energy-momentum; dimension: 2; AdS/CFT correspondence; field theory; boundary condition; conservation law; Burgers equation; energy levels; Wilson loop; family; circle

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Bruno Le Floch, Márk Mezei. Solving a family of $T\bar{T}$-like theories. 2019. ⟨hal-02088891⟩