Three Generations of SUSY Standard Model of Nambu-Goto String

Abstract

A four dimensional Superstring is constructed starting from a twenty six dimensional bosonic string. Fermions are introduced by noting the Manselstam's proof of equivalence of two fermions to one boson in 1+1 dimensions. The action of the superstring is invariant under SO(6)$\times$ SO(5). It has four bosonic coordinates and twenty four Majorana fermions of SO(3,1) representing two transverse modes of super fermions and conformal ghosts (b,c). The super conformal ghosts ($\beta, \gamma$) are the quanta of an extended Hilbert space of the remaining longitudinal modes of two superfermions. The massless spectrum obtained by quantising the action, contain vector mesons which are generators of the SO(6)$\times$SO(5). Using Wilson loops, this product group is proven to descend to $Z_3\times SU(3)\times SU(2)\times U(1)$ without breaking supersymmetry.Thus there are just three generations of quarks and leptons.