Superparticle models with tensorial central charges

Abstract

A generalization of the Ferber-Shirafuji formulation of superparticle mechanics is considered. The generalized model describes the dynamics of a superparticle in a superspace extended by tensorial central charge coordinates and commuting twistorlike spinor variables. The $D=4$ model contains a continuous real parameter $a>~0$ and at $a=0$ reduces to the $SU(2,2|1)$ supertwistor Ferber-Shirafuji model, while at $a=1$ one gets an $OSp(1|8)$ supertwistor model proposed by two of the authors which describes BPS states with all but one unbroken target space supersymmetries. When $0<a<1$ the model admits an $OSp(2|8)$ supertwistor description, and when $a>1$ the supertwistor group becomes $OSp(1,1|8).$ We quantize the model and find that its quantum spectrum consists of massless states of an arbitrary (half-)integer helicity. The independent discrete central charge coordinate describes the helicity spectrum. We also outline the generalization of the $a=1$ model to higher space-time dimensions and demonstrate that in $D=3,$ 4, 6, and 10, where the quantum states are massless, the extra degrees of freedom (with respect to that of the standard superparticle) parametrize compact manifolds. These compact manifolds can be associated with higher-dimensional helicity states. In particular, in $D=10$ the additional ``helicity'' manifold is isomorphic to the sphere ${S}^{7}.$