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

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 Poincaré 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).

34 pages

References in corpus (3)

• On non-abelian T-dual geometries with Ramond fluxes
• Non-abelian T-duality, Ramond Fields and Coset Geometries
• Strings in plane-fronted gravitational waves

Cited by in corpus (7)

• Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations
• 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
• Poisson-Lie identities and dualities of Bianchi cosmologies
• Jacobi-Lie Models and Supergravity Equations
• Plane-parallel waves as Jacobi-Lie models
• Non-Abelian target space duals of Thurston geometries