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

Abstract

Abstract We show that method of characteristics provides a powerful new point of view on $$ T\overline{T} $$ T T ¯ -and related deformations. Previously, the method of characteristics has been applied to $$ T\overline{T} $$ T 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 $$ T\overline{T} $$ T 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 $$ T\overline{T} $$ T T ¯ -deformation. We find the deformed Lagrangians for a class of $$ T\overline{T} $$ T T ¯ -like deformations in higher dimensions and the ($$ T\overline{T} $$ T T ¯ )α-deformation in 2d with generic α, generalizing recent results in [1] and [2].