Supersymmetric non-relativistic geometries in M-theory

TL;DR

This paper constructs M-theory supergravity solutions exhibiting non-relativistic Schrödinger symmetry, extending known geometries with supersymmetry and analyzing their properties and supersymmetry enhancement.

Contribution

It introduces new supersymmetric non-relativistic M-theory geometries with specific isometries and analyzes conditions for supersymmetry enhancement and particle number bounds.

Findings

Solutions have two supercharges generally, six in special cases.

The non-relativistic particle number is bounded by compact space quantum numbers.

A specific example with SU(2)xSU(2)xU(1) symmetry is studied.

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.