D-branes and non-Abelian T-duality

We study the effect of non-Abelian T-duality (NATD) on D-brane solutions of type II supergravity. Knowledge of the full brane solution allows us to track the brane charges and the corresponding brane configurations, thus providing justification for brane setups previously proposed in the literature and for the common lore that Dp brane solutions give rise to D(p+1)-D(p+3)-NS5 backgrounds under SU(2) NATD transverse to the brane. In brane solutions where spacetime is empty and flat at spatial infinity before NATD, the spatial infinity of the NATD is universal, i.e. independent of the initial brane configuration. Furthermore, it gives enough information to determine the ranges of all coordinates after NATD. In the more complicated examples of the D2 branes considered here, where spacetime is not asymptotically flat before NATD, the interpretation of the dual solutions remains unclear. In the case of supersymmetric D2 branes arising from M2 reductions to IIA on Sasaki-Einstein seven-manifolds, we explicitly verify that the solution obeys the appropriate generalized spinor equations for a supersymmetric domain wall in four dimensions. We also investigate the existence of supersymmetric mass-deformed D2 brane solutions.