Supersymmetric non-relativistic geometries in M-theory

TL;DR

This work constructs Schrödinger-invariant geometries in M-theory by starting from $\,\mathcal{N}=1$ warped $AdS_5$ backgrounds and implementing a nontrivial $U(1)$ bundle for the lightlike direction. The authors derive sufficient conditions for such deformations using harmonic (anti)self-dual two-forms on the internal base and analyze the resulting Killing spinors, showing two Poincaré supercharges generically and up to six in special cases when the parameter $\beta=0$. An explicit example with $M_4=S^2\times S^2$ and $SU(2)\times SU(2)\times U(1)$ symmetry demonstrates the construction and reveals a bound on non-relativistic particle number set by monopole-harmonic quantum numbers; the Kaluza-Klein spectrum is explored via the massive Klein-Gordon equation in the Schrödinger background. The paper also presents a non-supersymmetric Schrödinger solution with the same global symmetry, and discusses potential field-theory duals (e.g., non-relativistic mass-deformed ABJM) and broader implications for non-relativistic holography in M-theory.

Abstract

We construct M-theory supergravity solutions with the non-relativistic Schrodinger symmetry starting from the warped AdS_5 metric with N=1 supersymmetry. We impose the condition that the lightlike direction is compact by making it a non-trivial U(1) bundle over the compact space. Sufficient conditions for such solutions are analyzed. The solutions have two supercharges for generic values of parameters, but the number of supercharges increases to six in some special cases. A Schrodinger geometry with SU(2)xSU(2)xU(1) isometry is considered as a specific example. We consider the Kaluza-Klein modes and show that the non-relativistic particle number is bounded above by the quantum numbers of the compact space.