The Origin of Realistic Free Fermionic Models

All the realistic free fermionic models utilize a set of basis vectors, the NAHE set, that correspond to Z 2 × Z 2 orbifold compactification with nontrivial background fields. I argue that the realistic features of free fermionic models, like the number of generations and the fermion mass spectrum are due to the underlying Z 2 × Z 2 orbifold compactification. As a unified theory of gravity and the gauge interactions, heterotic string theory 1 should reproduce the matter and symmetry content of the Standard Model and determine the fermion mass spectrum. Presently we do not know what is the dynamical mechanism that selects the unique string vacuum, and, a priori, there is a large number of potentially viable superstring models. The notion, however, that there is a huge number of string models is somewhat misleading. By just imposing one or two phenomenological criteria, like three generations and a gauge group that can be reduced at low energies to the standard model gauge group, already one finds that the number of possibilities is substantially reduced. Imposing further phenomenological constraints may indeed single out a unique superstring model. If such a model is constructed, it will certainly be of use in trying to learn about the dynamical mechanism that chooses the string vacuum. The task of constructing phenomenologically viable string models seems hopeless. While in ten dimensions the string vacuum is more or less unique, in four dimensions there is a huge number of equivalent candidates. The string consistency constraints impose a number of degrees of freedom and those degrees of freedom produce a symmetry that is larger than the observed symmetry at low energies. Furthermore the number of chiral generations is also determined in the four dimensional vacuum and is correlated with the gauge degrees of freedom. A bottom–up approach, in which different blocks of the standard model are assembled together piece by piece, is not adequate. Rather, what is required is a top–bottom approach in which the features of the standard model are carved out of the more symmetric string vacua.