Plane-parallel waves as duals of the flat background

Abstract

We give a classification of non-Abelian T-duals of the flat metric in D=4 dimensions with respect to the four-dimensional continuous subgroups of the Poincare group. After dualizing the flat background, we identify majority of dual models as conformal sigma models in plane-parallel wave backgrounds, most of them having torsion. We give their form in Brinkmann coordinates. We find, besides the plane-parallel waves, several diagonalizable curved metrics with nontrivial scalar curvature and torsion. Using the non-Abelian T-duality, we find general solution of the classical field equations for all the sigma models in terms of d'Alembert solutions of the wave equation.

40 pages, results are compared with some added references

References in corpus (2)

• Strings in plane-fronted gravitational waves
• New solvable sigma models in plane--parallel wave background

Cited by in corpus (8)

• Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations
• Plane-parallel waves as duals of the flat background II: T-duality with spectators
• On uniqueness of T-duality with spectators
• Poisson-Lie T-plurality revisited. Is T-duality unique?
• Plane-parallel waves as duals of the flat background III: T-duality with torsionless $B$-field
• Non-Abelian T-duality of $Ad{S}_{d\le 3}$ families by Poisson-Lie T-duality
• Plane-parallel waves as Jacobi-Lie models
• Non-Abelian target space duals of Thurston geometries