Convex cones, Jordan algebras and the geometry of d=9 Maxwell-Einstein supergravity

Abstract

The authors show that the Riemannian manifold characterising the scalar field interactions of d=9 Maxwell-Einstein (ME) supergravity is the convex cone associated with a Jordan algebra of degree 2. The result is similar to that of a class of d=5, N=2, ME supergravity theories associated with Jordan algebras of degree 3. They also construct the unique irreducible d=9 Yang-Mills supergravity which has non-compact gauge group Sl(2; R).