The Fermion Generations Problem in the Gust in the Free World-Sheet Fermion Formulation
Abstract
In the framework of the four dimensional heterotic superstring with free fermions we present a revised version of the rank eight Grand Unified String Theories (GUST) which contain the
SU(3
)
H
-gauge family symmetry. We also develop some methods for building of corresponding string models. We explicitly construct GUST with gauge symmetry
G=SU(5)×U(1)×(SU(3)×U(1)
)
H
and
G=SO(10)×(SU(3)×U(1)
)
H
or
E(6)×SU(3
)
H
⊂E(8)
and consider the full massless spectrum for our string models. We consider for the observable gauge symmetry the diagonal subgroup
G
symm
of the rank 16 group
G×G
⊂SO(16)×SO(16)
or
⊂E(8)×E(8)
. We discuss the possible fermion matter and Higgs sectors in these theories. We study renormalizable and nonrenormolizable contributions to the superpotential. There has to exist "superweak" light chiral matter (
m
f
H
<
M
W
) in GUST under consideration. The understanding of quark and lepton mass spectra and family mixing leaves a possibility for the existence of an unusually low mass breaking scale of the
SU(3
)
H
family gauge symmetry (some TeV).