THE CONSTRUCTION OF REALISTIC 4-DIMENSIONAL STRINGS THROUGH ORBIFOLDS

We discuss the construction of "realistic" lower rank 4-dimensional strings, through symmetric orbifolds with background fields. We present Z3 three-generation SU(3) × SU(2) × U(1) models as well as models incorporating a left-right SU(2)L × SU(2)R × U(1)B-L symmetry in which proton stability is automatically guaranteed. Conformal field theory selection rules are used to find the flat directions to all orders which lead to these low-rank models and to study the relevant Yukawa couplings. A hierarchical structure of quark-lepton masses appears naturally in some models. We also present a detailed study of the structure of the Z3 × Z3 orbifold including the generalized GSO projection, the effect of discrete torsion and the conformal field theory Yukawa coupling selection rules. All these points are illustrated with a three-generation Z3 × Z3 model. We have made an effort to write a self-contained presentation in order to make this material available to non-string experts interested in the phenomenological aspects of this theory. © 1990.