Very-extended Kac-Moody algebras and their interpretation at low levels

TL;DR

This paper investigates very-extended Kac-Moody algebras, revealing their low-level generators align with the field content of gravity, forms, and scalars in reduced theories, and explores their Dynkin diagrams' encoding of duality information.

Contribution

It provides a detailed analysis of the low-level structure of very-extended Kac-Moody algebras and links their Dynkin diagrams to physical field content and dualities.

Findings

Low-level generators match bosonic field content in reduced theories.

Dynkin diagrams encode field content and generalized T-duality transformations.

Results support the algebraic structure's relevance to supergravity theories.

Abstract

We analyse the very-extended Kac-Moody algebras as representations in terms of certain A_d subalgebras and find the generators at low levels. Our results for low levels agree precisely with the bosonic field content of the theories containing gravity, forms and scalars which upon reduction to three dimensions can be described by a non-linear realisation. We explain how the Dynkin diagrams of the very-extended algebras encode information about the field content and generalised T-duality transformations.