Oxidation = group theory

Abstract

Dimensional reduction of theories involving (super)gravity gives rise to sigma models on coset spaces of the form G/H, with G being a non-compact group, and H its maximal compact subgroup. The reverse process, called oxidation, is the reconstruction of the possible higher-dimensional theories, given the lower-dimensional theory. In three dimensions, all degrees of freedom can be dualized to scalars. Given the group G for a three-dimensional sigma model on the coset G/H, we demonstrate an efficient method for recovering the higher-dimensional theories, essentially by decomposition into subgroups. The equations of motion, Bianchi identities, Kaluza–Klein modifications and Chern–Simons terms are easily extracted from the root lattice of the group G. We briefly discuss some aspects of oxidation from the E8(8)/SO(16) coset, and demonstrate that our formalism reproduces the Chern–Simons term of 11D supergravity, knows about the T-duality of IIA and IIB theory, and easily deals with self-dual tensors, like the 5-tensor of IIB supergravity.