Non-Relativistic Ten-Dimensional Minimal Supergravity

TL;DR

This paper develops a non-relativistic limit of ten-dimensional N=1 supergravity, revealing new symmetries and geometric structures, and discusses potential extensions to heterotic supergravity with Yang-Mills fields.

Contribution

It introduces a supersymmetric non-relativistic limit of ten-dimensional supergravity with novel geometric constraints and emergent symmetries, expanding the understanding of non-relativistic supergravity theories.

Findings

The non-relativistic action exhibits a local scale symmetry and two conformal supersymmetries.

Poisson and fermionic equations are derived via supersymmetry variations, not directly from the action.

Discussion of extending the framework to include Yang-Mills fields for heterotic supergravity.

Abstract

We construct a non-relativistic limit of ten-dimensional N=1 supergravity from the point of view of the symmetries, the action, and the equations of motion. This limit can only be realized in a supersymmetric way provided we impose by hand a set of geometric constraints, invariant under all the symmetries of the non-relativistic theory, that define a so-called `self-dual' Dilatation-invariant String Newton-Cartan geometry. The non-relativistic action exhibits three emerging symmetries: one local scale symmetry and two local conformal supersymmetries. Due to these emerging symmetries the Poisson equation for the Newton potential and two partner fermionic equations do not follow from a variation of the non-relativistic action but, instead, are obtained by a supersymmetry variation of the other equations of motion that do follow from a variation of the non-relativistic action. We shortly discuss the inclusion of the Yang-Mills sector that would lead to a non-relativistic heterotic supergravity action.