Schrodinger invariant solutions of type IIB with enhanced supersymmetry

TL;DR

This work constructs and classifies Killing spinors for Schrödinger-invariant Type IIB solutions with CY_3 cones over SE_5 bases, showing that generic SE_5 preserves six supersymmetries while special cases like the round S^5 enhance to twelve. The analysis identifies explicit spinor structures, derives the corresponding superisometry algebra, and demonstrates that two kinematical and two dynamical supersymmetries pair with two superconformal generators to realize a super-Schrödinger algebra, with Lie derivatives along the conformal generator generating the superconformal sector. The results elucidate how non-relativistic holography can accommodate enhanced supersymmetry and provide concrete geometric conditions (via W, h, and σ) for supersymmetry enhancement. The findings have potential implications for holographic descriptions of non-relativistic systems and motivate extensions to D=11 solutions and Schrödinger (z) generalizations.

Abstract

We construct the Killing spinors for a class of supersymmetric solutions of type IIB supergravity that are invariant under the non-relativistic Schrodinger algebra. The solutions depend on a five-dimensional Sasaki-Einstein space and it has been shown that they admit two Killing spinors. Here we will show that, for generic Sasaki-Einstein space, there are special subclasses of solutions which admit six Killing spinors and we determine the corresponding superisometry algebra. We also show that for the special case that the Sasaki-Einstein space is the round five-sphere, the number of Killing spinors can be increased to twelve.