SUPERSTRINGS WITH NEW SUPERSYMMETRY IN (9,2)-DIMENSION AND (10,2)-DIMENSION

We construct superstring theories that obey the new supersymmetry alge bra {Q(alpha),Q(beta)}=gamma(alpha beta)(mu nu)P(1 mu)P(2 nu) in a Gre en-Schwarz formalism, with kappa supersymmetry also of the new type. T he superstring is ina system with a superparticle so that their total momenta are P-2 mu, P-1 nu, respectively. The system is covariant and critical in (10,2) dimensions if the particle is massless and in (9,2) dimensions if the particle is massive. Both the superstring and super particle have coordinates with two timelike dimensions but each behave s effectively as if they have a single timelike dimension. This is due to gauge symmetries and associated constraints. We show how to genera lize the gauge principle to more intricate systems containing two part s, 1 and 2. Each part contains interacting constituents, such as p-bra nes, and each part behaves effectively as if they have one timelike co ordinate, although the full system has two timelike coordinates. The e xamples of two superparticles, and of a superparticle and a superstrin g, discussed in more detail are special cases of such a generalized in teracting system. [S0556-2821(97)07822-3].