Exceptional Groups and Physics

TL;DR

This paper explores the potential role of exceptional Lie groups in fundamental physics, examining their appearance in charge space and string theory, while addressing challenges in using them as space-time symmetries.

Contribution

It analyzes the relevance of exceptional groups like E6 and E8 in particle physics and string theory, proposing ways to incorporate them into supergravity frameworks.

Findings

E6 fits naturally within the Standard Model

E8×E8 appears in heterotic string theory

Challenges exist in using exceptional groups as space-time symmetries

Abstract

Quarks and leptons charges and interactions are derived from gauge theories associated with symmetries. Their space-time labels come from representations of the non-compact algebra of Special Relativity. Common to these descriptions are the Lie groups stemming from their invariances. Does Nature use Exceptional Groups, the most distinctive among them? We examine the case for and against their use. They do indeed appear in charge space, as the Standard Model fits naturally inside the exceptional group $E_6$. Further, the advent of the $E_8\times E_8$ Heterotic Superstring theory adds credibility to this venue. On the other hand, their use as space-time labels has not been as evident as they link spinors and tensors under space rotations, which flies in the face of the spin-statistics connection. We discuss a way to circumvent this difficulty in trying to generalize eleven-dimensional supergravity.