Three - Family Grand Unification in String Theory ∗ †

The outstanding question of string theory is whether it describes our universe. This question turns out to be very difficult to answer as the space of classical string vacua has a very large degeneracy, and there lack objective criteria that would select a particular string vacuum among the numerous possibilities. One might expect non-perturbative string dynamics to lift, partially or completely, this degeneracy in the moduli space. A priori it is reasonable to suspect that non-perturbative dynamics may not select the unique vacuum, but rather pick out a number of consistent vacua with completely broken supersymmetry. The reader might find the following analogy, that belongs to Henry Tye, amusing. The ancient Greeks, among many others, believed that the earth was the center of the universe, and everything else revolved around it. Just as this perception did not prove correct, it might be too naive to believe that the only truly consistent superstring vacuum is the one that describes our universe. If so, then to find the string vacuum where we live, we would need to impose some additional, namely, phenomenological constraints. This approach has been known as “superstring phenomenology”. The latter must still be augmented with understanding of non-perturbative dynamics as superstring is believed not to break supersymmetry perturbatively. The guiding principle of superstring phenomenology is very simple: it is to find a string model that within its effective low energy field theory will reproduce the Standard Model of