Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity Theories

TL;DR

This paper explores the potential Kac-Moody symmetries of ten-dimensional N=1 supergravity and its extensions, identifying specific very-extended algebras that could underlie these theories' symmetry structures.

Contribution

It demonstrates that extending N=1 supergravity to include certain symmetries involves specific very-extended Kac-Moody algebras, advancing understanding of supergravity symmetry frameworks.

Findings

Identifies a rank eleven Kac-Moody algebra related to supergravity extensions.

Connects N=1 supergravity coupled with abelian vectors to very-extended B_8.

Discusses the symmetry structure for theories with multiple abelian vectors.

Abstract

A description of the bosonic sector of ten-dimensional N=1 supergravity as a non-linear realisation is given. We show that if a suitable extension of this theory were invariant under a Kac-Moody algebra, then this algebra would have to contain a rank eleven Kac-Moody algebra, that can be identified to be a particular real form of very-extended D_8. We also describe the extension of N=1 supergravity coupled to an abelian vector gauge field as a non-linear realisation, and find the Kac-Moody algebra governing the symmetries of this theory to be very-extended B_8. Finally, we discuss the related points for the N=1 supergravity coupled to an arbitrary number of abelian vector gauge fields.