CERN-TH-97-187 PSU-TH-188 Orbits of Exceptional Groups, Duality and BPS States in String Theory

We give an invariant classi cation of orbits of the fundamental representations of exceptional groups E7(7) and E6(6) which classify BPS states in string and M theories toroidally compacti ed to d = 4 and 5. The exceptional Jordan algebra and the exceptional Freudenthal triple system and their cubic and quartic invariants play a major role in this classi cation. The cubic and quartic invariants correspond to the black hole entropy in d = 5 and d = 4, respectively. The classi cation of BPS states preserving di erent numbers of supersymmetries is in close parallel to the classi cation of the little groups and the orbits of timelike, lightlike and space-like vectors in Minkowski space. 1 Work supported in part by EEC under TMR contract ERBFMRX-CT96-00 (LNF Frascati, INFN, Italy) and DOE grant DE-FGO3-91ER40662, DE-FGO2-96ER40559 e-mail: [email protected] 2 Work supported in part by the National Science Foundation under Grant Number PHY-9631332. Permanent address: Penn State University, Physics Dept. University Park, PA 16802 e-mail: [email protected]