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The group theory of oxidation

Arjan Keurentjes
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Abstract

Dimensional reduction of (super-)gravity theories to 3 dimensions results in sigma models on coset spaces G/H, such as the E_8/SO(16) coset in the bosonic sector of 3 dimensional maximal supergravity. 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 E_n gravities, and approximate reflection symmetry of the older ``magic triangle'' of supergravities in 4 dimensions, are easily understood in this framework.

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Arjan Keurentjes. 2003-01-16. The group theory of oxidation. https://doi.org/10.1016/s0550-3213(03)00178-0

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