TY - JOUR
T1 - Tits-Satake projections of homogeneous special geometries
AU - Fré, Pietro
AU - Gargiulo, Floriana
AU - Rosseel, Jan
AU - Rulik, Ksenya
AU - Trigiante, Mario
AU - Van Proeyen, Antoine
PY - 2007/1/7
Y1 - 2007/1/7
N2 - We organize the homogeneous special geometries, describing as well the couplings of D = 6, 5, 4 and 3 supergravities with eight 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 into 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 class both in relation with cosmic billiard dynamics and with configurations of branes and orbifolds defining special geometry backgrounds.
AB - We organize the homogeneous special geometries, describing as well the couplings of D = 6, 5, 4 and 3 supergravities with eight 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 into 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 class both in relation with cosmic billiard dynamics and with configurations of branes and orbifolds defining special geometry backgrounds.
UR - http://www.scopus.com/inward/record.url?scp=33847638014&partnerID=8YFLogxK
U2 - 10.1088/0264-9381/24/1/003
DO - 10.1088/0264-9381/24/1/003
M3 - Article
AN - SCOPUS:33847638014
SN - 0264-9381
VL - 24
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
IS - 1
M1 - 003
ER -