Real forms of very extended Kac-Moody algebras and theories with eight supersymmetries

TL;DR

This paper explores the connection between theories with eight supersymmetries and very-extended Kac-Moody algebras, proposing that these theories can be described as their non-linear realisations, especially in three dimensions.

Contribution

It demonstrates that for key cases, the bosonic sector of supersymmetric theories matches the non-linear realisation of specific very-extended Kac-Moody algebras with appropriate real forms.

Findings

Bosonic sectors match non-linear realisations

Theories with eight supersymmetries are linked to Kac-Moody algebras

Conjecture supported by case studies

Abstract

We consider all theories with eight supersymmetries whose reduction to three dimensions gives rise to scalars that parametrise symmetric manifolds. We conjecture that these theories are non-linear realisations of very-extended Kac-Moody algebras for suitable choices of real forms. We show for the most interesting cases that the bosonic sector of the supersymmetric theory is precisely reproduced by the corresponding non-linear realisation.