Supersymmetric non-relativistic geometries in M-theory

We construct M-theory supergravity solutions with the non-relativistic Schrödinger symmetry starting from the warped AdS5AdS5 metric with N=1N=1 supersymmetry. We impose the condition that the lightlike direction is compact by making it a non-trivial U(1)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 Schrödinger geometry with SU(2)×SU(2)×U(1)SU(2)×SU(2)×U(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.