Solutions of type IIB and D=11 supergravity with Schrodinger(z) symmetry

TL;DR

The paper addresses constructing supersymmetric backgrounds in type IIB and $D=11$ supergravity that realize Sch$(z)$ symmetry for a range of dynamical exponents $z$, using Calabi–Yau cones over Sasaki–Einstein manifolds. The authors extend prior Donos–Gauntlett frameworks by turning on nontrivial flux components $C,h,W$ (IIB) and $C,h,V$ (D=11) and by tuning scaling exponents to achieve Schrödinger$(z)$ invariance on CY$_3$ and CY$_4$ cones, respectively. They present explicit families including $z=2$ solutions, discuss supersymmetry projections that preserve a fraction of Poincaré supersymmetry, and comment on stability in the presence of flux deformations. These results broaden the landscape of holographic non-relativistic duals with controlled supersymmetry, enabling more tractable analyses of dual condensed-matter-like systems.

Abstract

We construct families of supersymmetric solutions of type IIB and D=11 supergravity that are invariant under the non-relativistic Schrodinger(z) algebra for various values of the dynamical exponent z. The new solutions are based on five- and seven-dimensional Sasaki-Einstein manifolds, respectively, and include supersymmetric solutions with z=2.