String Models for Locally Supersymmetric Grand Unification

Phenomenologically viable string vacua may require incorporating Kac-Moody algebras at level $\geq 2$. We exploit the free fermionic formulation to construct N=(0,2) world-sheet supersymmetric string models with specific phenomenological input: N=1 spacetime supersymmetry, three generations of chiral fermions in gauge groups $SO(10)$ or $SU(5)$, adjoint Higgses, and a single Yukawa coupling of a fundamental Higgs to the third generation. In this talk, we will show models of gauge group $SO(10)$ and of $SU(5)$ without any gauge singlet moduli, and show some novel features appearing in the connection of these two models. The accompanying, and rather non-trivial, discrete chiral sub-algebras can determine hierarchies in the fermion mass matrix. Our approach to string phenomenology opens up the possibility of {\it concrete} explorations of a wide range of proposals both for dynamical supersymmetry breaking and for the dynamics of the dilaton and other stringy moduli. (Talk presented at DPF 94, Albuquerque, New Mexico)