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 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 3 dimensions, all degrees of freedom can be dualized to scalars. Given the group G for a 3 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 E_{8(8)}/SO(16) coset, and demonstrate that our formalism reproduces the Chern-Simons term of 11-d 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.
Cite
@article{arxiv.hep-th/0212050,
title = {Oxidation = group theory},
author = {Arjan Keurentjes},
journal= {arXiv preprint arXiv:hep-th/0212050},
year = {2009}
}
Comments
LaTeX, 8 pages, uses IOP style files; Talk given at the RTN workshop ``The quantum structure of spacetime and the geometric nature of fundamental interactions'', Leuven, September 2002