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 ppwaves, or generalized plane wave (K-model).
We investigate the dependence of nonabelian T-duality on various
identification of the group of target space isometries of nonlinear sigma
models with its orbits, i.e. with respect to the location of the group unit on
manifolds invariant under the isometry group. We show that T-duals constructed
by isometry groups of dimension less than the dimension of the
(pseudo)riemannian manifold may depend not only on the initial metric but also
on the choice of manifolds defining positions of group units on each of the
submanifold invariant under the isometry group. We investigate whether this
dependence can be compensated by coordinate transformation.Comment: 11 pages, an introductory example added, some typos correcte
By addition of non-zero, but torsionless B-field, we expand the classification of (non-)Abelian T-duals of the flat background in four dimensions with respect to one-, two-, three-, and four-dimensional subgroups of Poincaré group. We discuss the influence of the additional B-field on the process of dualization and identify essential parts of the torsionless B-field that cannot be eliminated in general by coordinate or gauge transformation of the dual background. These effects are demonstrated using particular examples. Due to their physical importance, we focus on duals whose metrics represent plane-parallel waves. Besides the previously found metrics, we find new pp-waves depending on parameters originating from the torsionless B-field. These pp-waves are brought into their standard forms in Brinkmann and Rosen coordinates. *
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