Englert-type solutions of d=11 supergravity

TL;DR

This paper explores a family of solutions to 11-dimensional supergravity equations involving geometries on S^7, including flat and non-flat torsion geometries characterized by nonassociative structures.

Contribution

It introduces new non-flat geometries with torsion in 11D supergravity, expanding the known solution space beyond conventional and flat geometries.

Findings

Identification of non-flat geometries with torsion on S^7

Use of nonassociative geodesic loops to describe torsion

Extension of known supergravity solutions

Abstract

A family of geometries on S^7 arise as solutions of the classical equations of motion in 11 dimensions. In addition to the conventional riemannian geometry and the two exceptional Cartan-Schouten compact flat geometries with torsion, one can also obtain non-flat geometries with torsion. This torsion is given locally by the structure constants of a nonassociative geodesic loop in the affinely connected space.