Non-relativistic supersymmetric Dp branes

The supergravity solutions to various $p$-branes are presented and typically it breaks one quarter of supersymmetry except for the D1 brane case, where it breaks one half of supersymmetry and are manifestly non-relativistic in nature. The symmetries that the solutions enjoys are that of space and time translations, rotations, boosts but without any scaling and special conformal transformations except for $p\mathrm{\ne }3$. We have also constructed supersymmetric non-relativistic cascading solutions to intersecting $D3$ and $D5$ branes on both the singular as well as on deformed conifold, where the $D5$’s are wrapped on the $S^2$ of the Calabi-Yau i.e. the analogs of Klebanov-Tseytlin and Klebanov-Strassler solutions and the supersymmetric non-relativistic M2 brane solution.