Classical solution of a sigma-model in curved background

TL;DR

This paper presents a method to solve a sigma-model in curved backgrounds by leveraging Poisson-Lie T-duality to transform the problem into a flat background, simplifying the solution process.

Contribution

It introduces an explicit approach to solve sigma-models in curved backgrounds using Poisson-Lie T-duality and coordinate transformations.

Findings

Successfully transformed curved background to flat background using T-duality.

Derived explicit solutions for the sigma-model in curved backgrounds.

Demonstrated the utility of coordinate transformations in simplifying complex models.

Abstract

We have solved a sigma-model in curved background using the fact that the Poisson-Lie T-duality can transform the curved background into the flat one. For finding solution of the flat model we have used transformation of coordinates that makes the metric constant. The T-duality transform was then explicitly performed.