Abstract :
Dimensional reduction of (super-)gravity theories to 3 dimensions results in sigma models on coset spaces G/H, such as the E8/SO(16) coset in the bosonic sector of 3-dimensional maximal super-gravity. 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 En gravities, and approximate reflection symmetry of the older “magic triangle” of super-gravities in 4 dimensions, are easily understood in this framework.
