Dirac's Footsteps and Supersymmetry

TL;DR

This paper explores the deep connections between Dirac's equation, supersymmetry, and string theory, proposing a group-theoretical interpretation of supergravity divergences and their potential link to M-theory.

Contribution

It introduces a novel perspective on supergravity divergences using group theory and higher spin fields, suggesting a pathway towards understanding M-theory.

Findings

Dirac's equation underpins supersymmetry and string theory.

Supergravity divergences may be explained by higher spin fields and group theory.

Potential implications for the development of M-theory.

Abstract

One hundred years after its creator's birth, the Dirac equation stands as the cornerstone of XXth Century physics. But it is much more, as it carries the seeds of supersymmetry. Dirac also invented the light-cone, or "front form" dynamics, which plays a crucial role in string theory and in elucidating the finiteness of N=4 Yang-Mills theory. The light-cone structure of eleven-dimensional supergravity (N=8 supergravity in four dimensions) suggests a group-theoretical interpretation of its divergences. We speculate they could be compensated by an infinite number of triplets of massless higher spin fields, each obeying a Dirac-like equation associated with the coset $F_4/SO(9)$. The divergences are proportional to the trace over a non-compact structure containing the compact form of $F_4$. Its nature is still unknown, but it could show the way to $M$-theory.