Nonabelian dualization of plane wave backgrounds

TL;DR

This paper explores the Poisson-Lie T-dualizability of plane-parallel wave metrics by reconstructing them as nonlinear sigma models on Lie groups, and finds dual backgrounds satisfying beta function equations.

Contribution

It introduces a method to obtain dual backgrounds of plane wave metrics using Drinfel'd doubles and explores a new form of T-plurality beyond standard Poisson-Lie T-plurality.

Findings

Dual backgrounds satisfy vanishing beta equations.

Invariant torsion potentials are constructed via Drinfel'd doubles.

Multiple dual backgrounds exist for certain isometry subgroups.

Abstract

We investigate plane-parallel wave metrics from the point of view of their (Poisson-Lie) T-dualizability. For that purpose we reconstruct the metrics as backgrounds of nonlinear sigma models on Lie groups. For construction of dual backgrounds we use Drinfel'd doubles obtained from the isometry groups of the metrics. We find dilaton fields that enable to satisfy the vanishing beta equations for the duals of the homogenous plane-parallel wave metric. Torsion potentials or B-fields, invariant w.r.t. the isometry group of Lobachevski plane waves are obtained by the Drinfel'd double construction. We show that a certain kind of plurality, different from the (atomic) Poisson-Lie T-plurality, may exist in case that metrics admit several isometry subgroups having the dimension of the Riemannian manifold. An example of that are two different backgrounds dual to the homogenous plane-parallel wave metric.