A Novel Superstring in Four Dimensions and Grand Unification

Abstract

A string in four dimensions is constructed by supplementing it with forty four Majorana fermions. The central charge is 26. The fermions are grouped in such a way that the resulting action is supersymmetric. The energy momentum and current generators satisfy the super-Virasoro algebra. The tachyonic ground state decouples from the physical states. GSO projections are necessary for proving modular invariance. Space-time supersymmetry provides reasons to discard the tachyons and is substantiated for modes of zero mass. The symmetry group of the model descends to the low energy standard model group $SU (3) \times SU_L (2) \times U_Y (1)$ through the Pati-Salam group. Left right symmetry is broken spontaneously and the mass of the tau neutrino is calculated to be about 1/25 electron volt.