Supersymmetric two-time physics

We construct an Sp(2, R) gauge invariant particle action which possesses manifest space-time SO(d, 2) symmetry, global supersymmetry and kappa supersymmetry. The global and local supersymmetries are non-Abelian generalizations of Poincare type supersymmetries and are consistent with the presence of two timelike dimensions. In particular, this action provides a unified and explicit superparticle representation of the superconformal groups OSp(N/4), SU(2,2/N) and OSp(8*/N) which underlie various AdS-CFT dualities in M or string theory. By making diverse Sp(2, R) gauge choices our action reduces to diverse one-time physics systems, one of which is the ordinary (one-time) massless superparticle with superconformal symmetry that we discuss explicitly. We show how to generalize our approach to the case of superalgebras, such as OSp(1/32), which do not have direct space-time interpretations in terms of only zero branes, but may be realizable in the presence of p-branes. [S0556-2821(99)03412-8].