On the geometry of the supermultiplet in M-theory

TL;DR

This paper explores the geometric structure of the supermultiplet in M-theory, focusing on the role of the Cayley plane and topological forms, and discusses its compatibility with string theories.

Contribution

It characterizes the geometric and topological forms related to the supermultiplet, including torsion and cohomology, and connects these structures to string theory reductions.

Findings

Identification of forms contributing to the action and partition function.

Analysis of torsion and cohomology classes in the geometric framework.

Discussion of compatibility with various string theories.

Abstract

The massless supermultiplet of eleven-dimensional supergravity can be generated from the decomposition of certain representation of the exceptional Lie group F4 into those of its maximal compact subgroup Spin(9). In an earlier paper, a dynamical Kaluza-Klein origin of this observation is proposed with internal space the Cayley plane, OP2, and topological aspects are explored. In this paper we consider the geometric aspects and characterize the corresponding forms which contribute to the action as well as cohomology classes, including torsion, which contribute to the partition function. This involves constructions with bilinear forms. The compatibility with various string theories are discussed, including reduction to loop bundles in ten dimensions.