Pure type I supergravity and DE(10)

TL;DR

This paper demonstrates a dynamical equivalence between pure type I supergravity in ten dimensions and a one-dimensional non-linear sigma-model based on the Kac-Moody algebra DE(10), using algebraic decompositions and truncations.

Contribution

It establishes a novel connection between supergravity and Kac-Moody algebra structures, extending the understanding of symmetries in supergravity theories.

Findings

Dynamical equivalence between supergravity and sigma-models on DE(10)/K(DE(10))

Use of SO(9,9) decomposition of DE(10)

Inclusion of fermionic fields and their representations

Abstract

We establish a dynamical equivalence between the bosonic part of pure type I supergravity in D=10 and a D=1 non-linear sigma-model on the Kac-Moody coset space DE(10)/K(DE(10)) if both theories are suitably truncated. To this end we make use of a decomposition of DE(10) under its regular SO(9,9) subgroup. Our analysis also deals partly with the fermionic fields of the supergravity theory and we define corresponding representations of the generalized spatial Lorentz group K(DE(10)).