Spontaneous compactification and nonassociativity

TL;DR

This paper explores the mechanisms of spontaneous compactification in 11-dimensional supergravity, revealing that three-form potentials relate to structure constants of geodesic loops, and investigates both known and new solutions.

Contribution

It introduces a novel geometric interpretation of three-form potentials as structure constants of geodesic loops in affinely connected spaces.

Findings

Identification of three-form potentials with geodesic loop structure constants

Systematic analysis of classical solutions in 11-dimensional supergravity

Discovery of new solutions beyond well-known compactifications

Abstract

We consider the Freund-Rubin-Englert mechanism of compactification of N=1 supergravity in 11 dimensions. We systematically investigate both well-known and some new solutions of the classical equations of motion in 11 dimensions. In particular, we show that any threeform potential in 11 dimension is given locally by the structure constants of a geodesic loop in an affinely connected space.