Plane-parallel waves as duals of the flat background II: T-duality with spectators

TL;DR

This paper classifies T-duals of four-dimensional flat backgrounds using non-Abelian T-duality with spectators, revealing various plane-parallel wave backgrounds, including exactly solvable and singular models.

Contribution

It provides a comprehensive classification of T-duals of flat four-dimensional backgrounds with respect to subgroups of the Poincaré group, introducing new solvable and singular plane wave solutions.

Findings

Identified T-duals as plane-parallel waves and curved metrics with torsion.

Discovered exactly solvable time-dependent isotropic pp-waves.

Found singular pp-waves and generalized plane wave solutions.

Abstract

We give the classification of T-duals of the flat background in four dimensions with respect to one-, two-, and three-dimensional subgroups of the Poincar\'e group using non-Abelian T-duality with spectators. As duals we find backgrounds for sigma models in the form of plane-parallel waves or diagonalizable curved metrics often with torsion. Among others, we find exactly solvable time-dependent isotropic pp-wave, singular pp-waves, or generalized plane wave (K-model).