Consistent supersymmetric Kaluza--Klein truncations with massive modes

TL;DR

This paper develops consistent Kaluza-Klein reductions of 11-dimensional supergravity on seven-dimensional manifolds, including massive modes, leading to new four-dimensional supergravity theories with potential applications in M-theory solutions.

Contribution

It extends known reductions to include massive fields and generalizes to Sasaki--Einstein and weak G_2 manifolds, providing new consistent truncations with supersymmetry.

Findings

Constructed N=2 supergravity with massive modes from Sasaki--Einstein reductions.

Extended to N=1 supergravity on weak G_2 manifolds with massive fields.

Provided solutions of M-theory with non-relativistic conformal symmetry.

Abstract

We construct consistent Kaluza--Klein reductions of D=11 supergravity to four dimensions using an arbitrary seven-dimensional Sasaki--Einstein manifold. At the level of bosonic fields, we extend the known reduction, which leads to minimal N=2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the Sasaki--Einstein space, and still consistent with N=2 supersymmetry. In the context of flux compactifications, the Sasaki--Einstein reductions are generalizations of type IIA SU(3)-structure reductions which include both metric and form-field flux and lead to a massive universal tensor multiplet. We carry out a similar analysis for an arbitrary weak G_2 manifold leading to an N=1 supergravity with massive fields. The straightforward extension of our results to the case of the seven-sphere would imply that there is a four-dimensional Lagrangian with N=8 supersymmetry containing both massless and massive spin two fields. We use our results to construct solutions of M-theory with non-relativistic conformal symmetry.