The Unification in the String Theories with the G × G Gauge Groups

Abstract

In the framework of the four-dimensional heterotic superstring with free fermions we discuss the rank eight and/or 16 Grand Unified String Theories (GUSTs) which contain the SU (3)H-gauge family symmetry. We explicitly investigate the paths of the unification in the GUST with gauge symmetry G × G = [ SU (5)× U (1)×( SU (3)× U (1))H]⊗2. We show that the GUSTs with the G × G gauge group allow one to make the scale of unification to be consistent with the string scale M SU ~ g str ×5×1017 GeV.