For most Thurston geometries, the paper constructs explicit non-Abelian T-dual metrics and B-fields via Poisson-Lie duality, yielding 20 string backgrounds.
Poisson-Lie T-Duality and Bianchi Type Algebras
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abstract
All Bianchi bialgebras have been obtained. By introducing a non-degenerate adjoint invariant inner product over these bialgebras the associated Drinfeld doubles have been constructed, then by calculating the coupling matrices for these bialgebras several sigma-models with Poisson-Lie symmetry have been obtained. Two simple examples as prototypes of Poisson-Lie dual models have been given.
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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.