Recently, Ferrara and Kallosh posted a paper on arxiv entitled Creation of Matter in the Universe and Groups of Type E7. The abstract is as follows:

We relate the mechanism of matter creation in the universe after inflation to a simple and universal mathematical property of extended N > 1 supergravities and related compactifications of superstring theory. We show that in all such models, the inflaton field may decay into vector fields due to a nonminimal scalar-vector coupling. This coupling is compulsory for all scalars except N=2 hyperscalars. The proof is based on the fact that all extended supergravities described by symmetric coset spaces G/H have duality groups G of type E7, with exception of U(p,n) models. For N=2 we prove separately that special geometry requires a non-minimal scalar-vector coupling. Upon truncation to N=1 supergravity, extended models generically preserve the non-minimal scalar-vector coupling, with exception of U(p,n) models and hyperscalars. For some string theory/supergravity inflationary models, this coupling provides the only way to complete the process of creation of matter in the early universe.

As mentioned in the article, one can consider d=4, N=8 supergravity arising from M-theory on T^7, with duality group G=E7(7) acting on a 56-dimensional Freudenthal triple system (FTS) over the split-octonions. Another type arises from the N=2 magic supergravity based on the FTS over the octonions, with duality group G=E7(-25). At an algebraic level, E7(7) and E7(-25) are unified in the complexified duality group G=E7(C) acting on the FTS over the bioctonions. There is, however, no corresponding E7(C) supergravity theory at this time.

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