Plane-parallel waves as duals of the flat background III: T-duality with torsionless $B$-field

TL;DR

This paper classifies T-duals of flat four-dimensional backgrounds with a torsionless B-field, revealing new plane-parallel wave solutions and analyzing how the B-field influences dualization processes.

Contribution

It extends the classification of T-duals by incorporating torsionless B-fields, identifying their effects on dual backgrounds, and discovering new pp-wave solutions.

Findings

New pp-wave metrics depending on B-field parameters

Identification of B-field components that cannot be gauged away

Enhanced classification of T-duals with torsionless B-fields

Abstract

By addition of non-zero, but torsionless $B$-field, we expand the classification of (non-)Abelian T-duals of the flat background in four dimensions with respect to one-, two-, three-, and four-dimensional subgroups of Poincar\'e group. We discuss the influence of the additional $B$-field on the process of dualization and identify essential parts of the torsionless $B$-field that cannot be eliminated in general by coordinate or gauge transformation of the dual background. These effects are demonstrated using particular examples. Due to their physical importance, we focus on duals whose metrics represent plane-parallel waves. Besides the previously found metrics, we find new pp-waves depending on parameters originating from the torsionless $B$-field. These pp-waves are brought into their standard forms in Brinkmann and Rosen coordinates.