1201.6314 (Sergio L. Cacciatori et al.)

Magic Coset Decompositions    [PDF]

Sergio L. Cacciatori, Bianca Letizia Cerchiai, Alessio Marrani

By exploiting a "mixed" non-symmetric Freudenthal-Rozenfeld-Tits magic
square, two types of coset decompositions are analyzed for the non-compact
special K\"ahler symmetric rank-3 coset E7(-25)/[(E6(-78) x U(1))/Z_3],
occurring in supergravity as the vector multiplets' scalar manifold in N=2, D=4
exceptional Maxwell-Einstein theory. The first decomposition exhibits maximal
manifest covariance, whereas the second (triality-symmetric) one is of Iwasawa
type, with maximal SO(8) covariance. Generalizations to minimally non-compact,
real forms of non-degenerate, simple groups "of type E7" are presented for both
classes of coset parametrizations, and relations to rank-3 simple Euclidean
Jordan algebras and normed trialities over division algebras are also
discussed.

View original: http://arxiv.org/abs/1201.6314