Consistent truncations of M-theory for general SU(2) structures

TL;DR

This paper develops a general framework for consistent truncations of M-theory on seven-dimensional manifolds with SU(2) structures, enabling reductions to N=4 gauged supergravity and unifying various special cases.

Contribution

It provides the first comprehensive SU(2) structure reduction of M-theory, relating torsion classes and fluxes to gaugings, and proves the consistency of this truncation.

Findings

Establishes a general SU(2) reduction framework for M-theory.

Shows the reduction is a consistent truncation solving 11D equations.

Unifies previous reductions on Tri-Sasakian and Calabi-Yau manifolds.

Abstract

In seven dimensions any spin manifold admits an SU(2) structure and therefore very general M-theory compactifications have the potential to allow for a reduction to N=4 gauged supergravity. We perform this general SU(2) reduction and give the relation of SU(2) torsion classes and fluxes to gaugings in the N=4 theory. We furthermore show explicitly that this reduction is a consistent truncation of the eleven-dimensional theory, in other words classical solutions of the reduced theory also solve the eleven-dimensional equations of motion. This reduction generalizes previous M-theory reductions on Tri-Sasakian manifolds and type IIA reductions on Calabi-Yau manifolds of vanishing Euler number. Moreover, it can also be applied to compactifications on certain G2 holonomy manifolds and to more general flux backgrounds.