Orbits of Exceptional Groups, Duality and BPS States in String Theory

TL;DR

This paper classifies the orbits of fundamental representations of exceptional groups related to BPS states in string and M theories, using invariants from Jordan algebras and Freudenthal systems, linking to black hole entropy.

Contribution

It provides an invariant classification of BPS states in string and M theories using exceptional group orbits and algebraic invariants, extending understanding of black hole entropy and supersymmetry.

Findings

Classifies BPS states via exceptional group orbits.

Connects invariants to black hole entropy in 4D and 5D.

Includes classification for theories with exceptional symmetry groups.

Abstract

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.