M(ysterious) Patterns in SO(9)

TL;DR

This paper explores the mathematical structure of SO(9) representations in eleven-dimensional supergravity, revealing a pattern of infinite families linked to the exceptional group F4, suggesting new insights into higher spin states.

Contribution

It uncovers a novel infinite family pattern of SO(9) representations related to F4 embeddings, extending understanding of supergravity degrees of freedom.

Findings

Identification of four-fold infinite families of representations

Connection between SO(9) embeddings and F4

Implications for higher spin state classification

Abstract

The light-cone little group, SO(9), classifies the massless degrees of freedom of eleven-dimensional supergravity, with a triplet of representations. We observe that this triplet generalizes to four-fold infinite families with the quantum numbers of massless higher spin states. Their mathematical structure stems from the three equivalent ways of embedding SO(9) into the exceptional group $F_4$.