THREE GENERATIONS OF SUSY STANDARD MODEL OF NAMBU–GOTO STRING

Abstract

A four-dimensional superstring have been constructed starting from a 26-dimensional bosonic string. Fermions are introduced by noting the Mandelstam's proof of equivalence of two fermions to one boson in 1+1 dimensions. The action of the superstring is invariant under SO (6) ⊗ SO (5) in the worldsheet. It has four bosonic coordinates and 44 Majorana fermions of SO (3, 1). Here the superstring action is shown to be invariant under conformal and superconformal transformations with the usual conformal and superconformal ghosts of the ten-dimensional superstrings. The massless spectrum obtained by quantizing the action, contain vector mesons which are generators of the SO (6) ⊗ SO (5). Using Wilson loops, this product group is proven to descend to Z3 ⊗ SU (3) ⊗ SU (2) ⊗ U (1) without breaking supersymmetry. Thus there are just three generations of quarks and leptons.