The surprising structure of non-relativistic 11-dimensional supergravity

TL;DR

This paper explores a non-relativistic limit of 11-dimensional supergravity, revealing a membrane Newton-Cartan geometry and analyzing the constraints needed for supersymmetry, with implications for non-relativistic holography.

Contribution

It introduces a novel non-relativistic limit of 11D supergravity, detailing the constraint structures for different supersymmetry counts and their implications.

Findings

Existence of supersymmetric solutions including non-relativistic M2 backgrounds.

Constraint sequences terminate after three derivatives of bosonic fields.

Unusual supersymmetry algebra realization without closure into diffeomorphisms.

Abstract

We study a non-relativistic limit of 11-dimensional supergravity. This limit leads to a theory with an underlying membrane Newton-Cartan geometry. Consistency of the non-relativistic limit requires the imposition of constraints, requiring that certain bosonic and fermionic torsions and curvatures vanish. We investigate the implications of two versions of these constraints. In one version, we keep only 16 supersymmetry transformations, leading to a simple (purely bosonic) constraint structure but an unusual realisation of the supersymmetry algebra which does not close into diffeomorphisms. In the other, we keep all 32 supersymmetry transformations. This requires a complicated sequence of bosonic and fermionic constraints, eventually involving three derivatives of bosonic fields. We argue, with a linearised calculation, that this sequence of constraints terminates. Furthermore, we show that there exists a family of supersymmetric solutions satisfying these constraints, containing the non-relativistic limit of the M2 supergravity solution recently obtained by Lambert and Smith as a background relevant for non-relativistic holography.