Algebraic Dreams

TL;DR

This paper explores the connection between exceptional mathematical structures, specifically the coset F_4/SO(9), and eleven-dimensional M-theory, proposing a potential generalization of supergravity and linking algebraic structures to fundamental physics.

Contribution

It introduces a novel connection between the coset F_4/SO(9), the Exceptional Jordan Algebra, and M-theory, suggesting new algebraic frameworks for understanding space-time in eleven dimensions.

Findings

Identification of the coset F_4/SO(9) with the projective space of the Exceptional Jordan Algebra

Proposal of a generalization of eleven-dimensional supergravity based on these structures

Linking algebraic structures to fundamental degrees of freedom in M-theory

Abstract

Nature's attraction to unique mathematical structures provides powerful hints for unraveling her mysteries. None is at present as intriguing as eleven-dimensional M-theory. The search for exceptional structures specific to eleven dimensions leads us to exceptional groups in the description of space-time. One specific connection, through the coset $F_4/SO(9)$, may provide a generalization of eleven-dimensional supergravity. Since this coset happens to be the projective space of the Exceptional Jordan Algebra, its charge space may be linked to the fundamental degrees of freedom underlying M-theory.