Magic Coset Decompositions
Abstract
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 conformal 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.
Keywords
Cite
@article{arxiv.1201.6314,
title = {Magic Coset Decompositions},
author = {Sergio L. Cacciatori and Bianca Letizia Cerchiai and Alessio Marrani},
journal= {arXiv preprint arXiv:1201.6314},
year = {2015}
}
Comments
34 pages, 1 figure, 7 tables; Improved presentation