Generations Of Chiral Fermions Research Articles

Chiral fermions and the witten index for the compactified heterotic string

It is demonstrated that, for the compactified heterotic superstring, the number of chiral fermion generations is determined by the Witten index of a related two-dimensional N = 1 supersymmetric σ-model.

Chiral fermion generations from higher-dimensional gravity

We discuss a six-dimensional SO(12) gauge theory which can be obtained from pure gravity in 18 dimensions coupled to a Majorana-Weyl spinor, if the ground state is characterized by a noncompact internal space without boundary with small finite volume. The six-dimensional SO(12) theory spontaneously compactifies to a four-dimensional SO(10) theory with local generation group SU(2) G × U(1) G. We obtain an even number of chiral fermion generations transforming as ( 16, k, ± 1 2 ) under SO(10) × SU(2) G × U(1) G. Adding a scalar field to the six-dimensional theory provides us with fields carrying all the quantum numbers needed for a realistic spontaneous symmetry breakdown to SU(3) c × U(1) e.m.

Spinors: Special embedding of colour and chiral fermions

Special embedding of colour in an SO(18) complex spinor is analyzed in an attempt to incorporate chiral fermion generations. We obtain five normal generations. In addition, there are Q = 5 3 , −4 3 colour triplet quarks and a doubly charged lepton. We also have shiny quarks (colour sextets and octets). The unification scale is extremely low (3 × 10 6 GeV) and there exists a low mass magnetic monopole.