Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-06-19
Class.Quant.Grav.24:27-78,2007
Physics
High Energy Physics
High Energy Physics - Theory
65 pages, LaTeX; v2: added reference; v3: small corrections, section 3.3 modified
Scientific paper
10.1088/0264-9381/24/1/003
We organize the homogeneous special geometries, describing as well the couplings of D=6, 5, 4 and 3 supergravities with 8 supercharges, in a small number of universality classes. This relates manifolds on which similar types of dynamical solutions can exist. The mathematical ingredient is the Tits-Satake projection of real simple Lie algebras, which we extend to all solvable Lie algebras occurring in these homogeneous special geometries. Apart from some exotic cases all the other, 'very special', homogeneous manifolds can be grouped in seven universality classes. The organization of these classes, which capture the essential features of their basic dynamics, commutes with the r- and c-map. Different members are distinguished by different choices of the paint group, a notion discovered in the context of cosmic billiard dynamics of non maximally supersymmetric supergravities. We comment on the usefulness of this organization in universality classes both in relation with cosmic billiard dynamics and with configurations of branes and orbifolds defining special geometry backgrounds.
Fre' Pietro
Gargiulo Floriana
Proeyen Antoine Van
Rosseel Jan
Rulik Ksenya
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