Simple space-time symmetries: Generalizing conformal field theory
- II. Institut fuer Theoretische Physik, Universitaet Hamburg, D-22761 Hamburg (Germany)
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 set-membership sign M is the identity component of a parabolic subgroup of G, implying factorization H=MAN{sup -}, where M generalizes Lorentz transformations, A dilatations, and N{sup -} special conformal transformations. (2) Special conformal transformations {xi} set-membership sign N{sup -} act trivially on tangent vectors v set-membership sign T{sub o}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{sub 7(-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 Guenaydin [Mod. Phys. Lett. A 8, 1407 (1993)]. 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 an automorphism with properties appropriate for a time reflection.
- OSTI ID:
- 20929710
- Journal Information:
- Journal of Mathematical Physics, Vol. 48, Issue 5; Other Information: DOI: 10.1063/1.2713999; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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