KK-monopoles and G-structures in M-theory/type IIA reductions

TL;DR

This paper explores the description of KK-monopoles in M-theory and type IIA reductions using G-structures and intrinsic torsion, extending the understanding of twisted reductions beyond traditional constraints.

Contribution

It establishes a correspondence between higher-dimensional backgrounds with KK-monopoles and four-dimensional supergravity data via G-structures, relaxing Jacobi constraints.

Findings

Derived the link between 4D data and torsion classes.

Confirmed the correspondence between higher-dimensional equations and 4D supergravity.

Extended the framework to include non-Jacobi constrained twisted reductions.

Abstract

We argue that M-theory/massive IIA backgrounds including KK-monopoles are suitably described in the language of G-structures and their intrinsic torsion. To this end, we study classes of minimal supergravity models that admit an interpretation as twisted reductions in which the twist parameters are not restricted to satisfy the Jacobi constraints $\omega\, \omega=0$ required by an ordinary Scherk-Schwarz reduction. We first derive the correspondence between four-dimensional data and torsion classes of the internal space and, then, check the one-to-one correspondence between higher-dimensional and four-dimensional equations of motion. Remarkably, the whole construction holds regardless of the Jacobi constraints, thus shedding light upon the string/M-theory interpretation of (smeared) KK-monopoles.