5 research outputs found
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 a point in 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 in N act trivially on
tangent vectors to the space-time manifold M. The allowed simple Lie groups G
are the universal coverings of SU(m,m), SO(2,D), Sp(l,R), SO*(4n) and E_7(-25)
and H are particular maximal parabolic subgroups. They coincide with the groups
of fractional linear transformations of Euklidean Jordan algebras whose use as
generalizations of Minkowski space time was advocated by Gunaydin. All these
groups G admit positive energy representations. It will also be shown that the
classical conformal groups SO(2,D) are the only allowed groups which possess a
time reflection automorphism; in all other cases space-time has an intrinsic
chiral structure.Comment: 37 pages, 4 Table