Gauge principles for multi-superparticles

Abstract

We formulate new gauge principles for n supersymmetric particles in a worldline formalism with N supersymmetries. The models provide realizations of the more general supersymmetries that are encountered in sectors of S-theory or Matrix theory, with a superalgebra of the form QαA,QβB=δABγαβμ1⋯μn(pμ11⋯pμnn). Due to the local gauge and kappa symmetries the n superparticle momenta piμ and N supercharges QαA are constrained by pi·pj=0 and γ·piQA=0. The constraints have solutions only in a space with n timelike dimensions and SOd+n−2,n spacetime symmetry. The cases SO(9,1), SO(10,2) and SO(10,3), with one, two and three timelike dimensions respectively, are of special interest. In each case, due to the constraints, the classical motion and quantum theory of each superparticle are equivalent to the physics with a single time-like dimension in an effective 10D superspace with SO9,1 Lorentz symmetry.