Oxidation = group theory

TL;DR

This paper presents a method to reconstruct higher-dimensional theories from three-dimensional sigma models based on coset spaces, utilizing group theory decomposition to recover equations and terms like Chern-Simons.

Contribution

It introduces an efficient group-theoretic approach for oxidation, enabling reconstruction of higher-dimensional supergravity theories from lower-dimensional models.

Findings

Reproduces the Chern-Simons term of 11-d supergravity

Identifies T-duality between IIA and IIB theories

Handles self-dual tensors in supergravity

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.