Massless Particles, Orthosymplectic Symmetry and Another Type of Kaluza-Klein Theory

Abstract

The superalgebra osp(8/l) is intimately related to the twistor program. Its most singular representation has the following property: restricted to the conformal subalgebra it contains each and every massless representation exactly once. In other words, one irreducible representation of osp(8/l) describes all massless particles with maximal efficiency. It is believed that such unification is required if massless fields of high spins are to have self-consistent interactions. There are other reasons for studying massless particles of all spins simultaneously. There is a very appealing model in which massless particles are viewed as states of two so(3,2) singletons. The astounding fact is that all free two-singleton states are precisely massless. The most singular representation of osp(8/2) is irreducible on osp(8/l) and completely determined by the latter representation. It finds direct application in supergravity theories. The most interesting Sp(8/R) homogeneous space is 10-dimensional. The action of the conformal subgroup leaves invariant a unique 4-dimensional submanifold that can be identified with space time. Kaluza-Klein expansion of the scalar field on 10-space, around this 4-dimensional manifold, leads to a field theory of massless particles with all integer spins on space time. A supersymmetric extension is also possible.