$T\bar{T}$ deformation of classical Liouville field theory

TL;DR

This paper explores the effects of the $Tar T$ deformation on classical Liouville field theory, analyzing its exact action, equations of motion, conserved currents, and vacuum solutions.

Contribution

It provides the first detailed study of the $Tar T$ deformation in classical Liouville theory, including explicit conserved currents and vacuum solutions.

Findings

Derived the exact deformed action and equations of motion.

Constructed an infinite set of conserved currents.

Identified vacuum solutions of the deformed theory.

Abstract

We consider the irrelevant flow of classical Liouville field theory driven by the $T\bar T$ operator. After discussing properties of its exact action and equation of motion we construct an infinite set of conserved currents. We also find its vacuum solutions.