Oxidation =group theory

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 threedimensional 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 Tduality of IIA and IIB theory, and easily deals with self-dual tensors, like the 5-tensor of IIB supergravity.