The group theory of oxidation

TL;DR

This paper explores how the group theory underlying coset sigma models in 3D supergravity can be used to reconstruct higher-dimensional gravity theories, revealing deep connections between group structures, dualities, and matter content.

Contribution

It introduces a group-theoretic framework for the process of oxidation, showing how equations of motion and dualities can be derived from the structure of the group G and its subgroups.

Findings

Reconstruction of higher-dimensional models from group decompositions.

Encoding of matter content and dualities via extended Dynkin diagrams.

Explanation of reflection symmetries in magic triangles through group theory.

Abstract

Dimensional reduction of (super-)gravity theories to 3 dimensions results in sigma models on coset spaces G/H, such as the E_8/SO(16) coset in the bosonic sector of 3 dimensional maximal supergravity. The reverse process, oxidation, is the reconstruction of a higher dimensional gravity theory from a coset sigma model. Using the group G as starting point, the higher dimensional models follow essentially from decomposition into subgroups. All equations of motion and Bianchi identities can be directly reconstructed from the group lattice, Kaluza-Klein modifications and Chern-Simons terms are encoded in the group structure. Manipulations of extended Dynkin diagrams encode matter content, and (string) dualities. The reflection symmetry of the ``magic triangle'' for E_n gravities, and approximate reflection symmetry of the older ``magic triangle'' of supergravities in 4 dimensions, are easily understood in this framework.