Supersymmetric solutions for non-relativistic holography

TL;DR

This work constructs new supersymmetric non-relativistic holographic backgrounds in type IIB and D=11 supergravity by deforming AdS$\times$SE geometries with one-forms on Calabi–Yau cones over Sasaki–Einstein spaces. The dynamical exponent $z$ is controlled by Laplacian eigenmodes on $SE_5$ and $SE_7$, yielding $z=1+\sqrt{1+\mu}$ (IIB) with $\mu\ge 8$, and $z=1+\tfrac{1}{2}\sqrt{4+\mu}$ (D=11) with $\mu\ge 12$, thereby producing families with $z\ge 4$ and $z\ge 3$ respectively; special cases recover the known $z=4$ IIB and $z=3$ D=11 solutions and can be extended to $z= l+3$ on $S^5$ and $z=(s+5)/2$ on $S^7$. Supersymmetry is carefully analyzed, showing that two Poincaré supercharges are generically preserved (eight for $S^5$ or $S^7$ in certain setups), while skew-whiffed versions break supersymmetry. The authors also present a generalisation combining harmonic deformations to obtain additional NR-symmetric backgrounds, linking to earlier scalar- and vector-mode constructions and expanding the landscape of holographic duals for non-relativistic systems.

Abstract

We construct families of supersymmetric solutions of type IIB and D=11 supergravity that are invariant under the non-relativistic conformal algebra for various values of dynamical exponent z greater than or equal to 4 and 3, respectively. The solutions are based on five- and seven-dimensional Sasaki-Einstein manifolds and generalise the known solutions with dynamical exponent z=4 for the type IIB case and z=3 for the D=11 case, respectively.