Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-08-05
Int.J.Mod.Phys.A13:2075-2088,1998
Physics
High Energy Physics
High Energy Physics - Theory
New references and two tables added, a new section on the orbits of N=2 Maxwell-Einstein supergravity theories in d=4 and d=5
Scientific paper
10.1142/S0217751X98000913
We give an invariant classification of orbits of the fundamental representations of exceptional groups $E_{7(7)}$ and $E_{6(6)}$ which classify BPS states in string and M theories toroidally compactified to d=4 and d=5. The exceptional Jordan algebra and the exceptional Freudenthal triple system and their cubic and quartic invariants play a major role in this classification. The cubic and quartic invariants correspond to the black hole entropy in d=5 and d=4, respectively. The classification of BPS states preserving different numbers of supersymmetries is in close parallel to the classification of the little groups and the orbits of timelike, lightlike and space-like vectors in Minkowski space. The orbits of BPS black holes in N=2 Maxwell-Einstein supergravity theories in d=4 and d=5 with symmetric space geometries are also classified including the exceptional N=2 theory that has $E_{7(-25)}$ and $E_{6(-26)}$ as its symmety in the respective dimensions.
Ferrara Sergio
Gunaydin Murat
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