Abstract
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.
Highlights
Non-Abelian T-duality (NATD) has recently attracted renewed interest, not least as a tool for generating new supergravity solutions
The near horizon limit of the D2 brane solution we study in section 4 corresponds to the massless limit and provides a simple solution to these supersymmetry equations in the case of SU(3) structure
The NATD of the spatial infinity limit of standard intersecting brane solutions is universal: it is given by a continuous linear distribution of NS5 branes along a half line with specific charge density
Summary
Non-Abelian T-duality (NATD) has recently attracted renewed interest, not least as a tool for generating new supergravity solutions. Before NATD, standard intersecting brane solutions (i.e. those following the simple harmonic superposition rule) often interpolate between two asymptotic regions, each of which is an independent supergravity solution in its own right: flat space at spatial infinity, and the near-horizon limit –which in the examples considered here always contains an AdS factor. As previously stated, both limits are genuine solutions so that NATD will generate new solutions out of them These will be called respectively the spatial infinity and near-horizon limit of the dual. One of our main motivations in deriving these supersymmetric domain wall equations was to search for the brane solution, if it exists, whose near horizon limit corresponds to the massive IIA solution found in [16]. In the appendix we explain our various conventions and compare them to the literature
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