Simple space-time symmetries: Generalizing conformal field theory

We study simple space-time symmetry groups G which act on a space-time manifold M=G∕H which admits a G-invariant global causal structure. We classify pairs (G,M) which share the following additional properties of conformal field theory. (1) The stability subgroup H of o∊M is the identity component of a parabolic subgroup of G, implying factorization H=MAN−, where M generalizes Lorentz transformations, A dilatations, and N− special conformal transformations. (2) Special conformal transformations ξ∊N− act trivially on tangent vectors v∊ToM. The allowed simple Lie groups G are the universal coverings of SU(m,m),SO(2,D),Sp(l,R),SO*(4n), and E7(−25) and H are particular maximal parabolic subgroups. They coincide with the groups of fractional linear transformations of Euclidean Jordan algebras whose use as generalizations of Minkowski space-time was advocated by Gunaydin [Mod. Phys. Lett. A 8, 1407 (1993)]. All these groups G admit positive energy representations. It will also be shown that the classical confor...