$T\bar T$-deformations in closed form

TL;DR

This paper provides a closed-form solution for the $T\bar{T}$-deformation of 2D quantum field theories and extends the approach to higher dimensions using algebraic metric dependence and Burgers' equation solutions.

Contribution

It introduces a method to integrate $T\bar{T}$-deformations exactly in closed form, including higher-dimensional extensions, when the action depends algebraically on the metric.

Findings

Closed-form solutions for $T\bar{T}$-deformations in 2D.

Extension of solutions to higher dimensions.

Connection to Burgers' equation for deformation integration.

Abstract

We consider the problem of exact integration of the $T\bar{T}$-deformation of two dimensional quantum field theories, as well as some higher dimensional extensions in the form of $\det T$-deformations. When the action can be shown to only depend algebraically on the background metric the solution of the deformation equation on the Lagrangian can be given in closed form in terms of solutions of the (extended) Burgers' equation. We present such examples in two and higher dimensions.