T T ¯ $$ T\overline{T} $$ flow as characteristic flows

Abstract

Abstract We show that method of characteristics provides a powerful new point of view on T T ¯ $$ T\overline{T} $$ -and related deformations. Previously, the method of characteristics has been applied to T T ¯ $$ T\overline{T} $$ -deformation mainly to solve Burgers’ equation, which governs the deformation of the quantum spectrum. In the current work, we study classical deformed quantities using this method and show that T T ¯ $$ T\overline{T} $$ flow can be seen as a characteristic flow. Exploiting this point of view, we re-derive a number of important known results and obtain interesting new ones. We prove the equivalence between dynamical change of coordinates and the generalized light-cone gauge approaches to T T ¯ $$ T\overline{T} $$ -deformation. We find the deformed Lagrangians for a class of T T ¯ $$ T\overline{T} $$ -like deformations in higher dimensions and the ( T T ¯ $$ T\overline{T} $$ ) α -deformation in 2d with generic α, generalizing recent results in [1] and [2].

Keywords

• Field Theories in Lower Dimensions
• Integrable Field Theories