Real forms of extended Kac-Moody symmetries and higher spin gauge theories

TL;DR

This paper explores the connection between higher spin gauge fields and real Kac-Moody algebras derived from extensions of finite-dimensional simple algebras, revealing most generators do not correspond to propagating higher spin fields.

Contribution

It provides a comprehensive classification of extended Kac-Moody algebras related to gravity reductions and proves that only finitely many generators correspond to propagating higher spin fields.

Findings

Most generators are non-propagating fields.

No higher spin fields are contained in the Kac-Moody algebra.

Complete list of extended Kac-Moody algebras and their properties.

Abstract

We consider the relation between higher spin gauge fields and real Kac-Moody Lie algebras. These algebras are obtained by double and triple extensions of real forms g_0 of the finite-dimensional simple algebras g arising in dimensional reductions of gravity and supergravity theories. Besides providing an exhaustive list of all such algebras, together with their associated involutions and restricted root diagrams, we are able to prove general properties of their spectrum of generators with respect to a decomposition of the triple extension of g_0 under its gravity subalgebra gl(D,R). These results are then combined with known consistent models of higher spin gauge theory to prove that all but finitely many generators correspond to non-propagating fields and there are no higher spin fields contained in the Kac-Moody algebra.