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Plane-parallel waves as duals of the flat background
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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.
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Cited by 2 Pith papers
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Eight-dimensional Manin triples, Yang-Baxter deformations and solutions of Supergravity Equations
Poisson-Lie T-plurality on decompositions of Drinfeld doubles from Manin triples yields curved backgrounds with torsion solving generalized supergravity equations, many interpretable as homogeneous Yang-Baxter deformations.
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Non-Abelian target space duals of Thurston geometries
For most Thurston geometries, the paper constructs explicit non-Abelian T-dual metrics and B-fields via Poisson-Lie duality, yielding 20 string backgrounds.
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