Scalar Supersymmetry in Bi-Spinor Gauge Theory

Abstract

We describe a new realization of both global and local supersymmetry acting in spaces of commuting and anticommuting differential forms. Unlike the standard supersymmetry, it has Lorentz scalar transformation parameters. It is related but is not reducible to standard supersymmetry. Reformulation of the Standard Model with the new supersymmetry, called scalar supersymmetry, can be achieved with the particle content of the SM. BRST symmetry is extended to include scalar supersymmetry multiplets. Linear realization of scalar supersymmetry with free fields or with fields interacting with background gravity is described. Gauge interactions require non-linear realizations of scalar supersymmetry and, except for SU(2), non-linear gauge-fixing conditions. Requiring scalar supersymmetry of interacting action with the simplest chiral multiplet can reduce the dynamical content of the theory to that of the SM: one complex scalar, gauge fields, and three generations of Weyl spinors. At low energies scalar supersymmetry is explicitly broken by gauge interactions. However, in the asymptotically free case it becomes exact in the ultraviolet limit. Thus it has the two most desirable features of softly broken standard supersymmetry built in. Implementation of exact scalar supersymmetry in an interacting string action is given.