New solvable sigma models in plane--parallel wave background

TL;DR

This paper explicitly solves string equations of motion in non-abelian T-dual backgrounds of plane-parallel waves, revealing new solvable models and their relation to more general wave backgrounds.

Contribution

It provides explicit solutions for string dynamics in novel non-abelian T-dual backgrounds using Poisson-Lie transformations, expanding solvable models in string theory.

Findings

Dual backgrounds can be transformed into more general plane-parallel waves.

Explicit solutions for string equations in these backgrounds are obtained.

Dual models are constructed using semi-abelian Drinfeld doubles.

Abstract

We explicitly solve the classical equations of motion for strings in backgrounds obtained as non-abelian T-duals of a homogeneous isotropic plane-parallel wave. To construct the dual backgrounds, semi-abelian Drinfeld doubles are used which contain the isometry group of the homogeneous plane wave metric. The dual solutions are then found by the Poisson-Lie transformation of the explicit solution of the original homogeneous plane wave background. Investigating their Killing vectors, we have found that the dual backgrounds can be transformed to the form of more general plane-parallel waves.