Heterotic coset models and (0, 2) string vacua

A Lagrangian definition of a large family of (0, 2) supersymmetric conformal field theories may be made by an appropriate gauge invariant combination of a gauged Wess-Zumino-Witten model, right-moving supersymmetry fermions, and left-moving current algebra fermions. Throughout this paper, use is made of the interplay between field theoretic and algebraic techniques (together with supersymmetry) which is facilitated by such a definition. These heterotic coset models are thus studied in some detail, with particular attention paid to the (0,2) analogue of the N = 2 minimal models, which coincide with the 'monopole' theory of Giddings, Polchinski and Strominger. A family of modular invariant partition functions for these (0, 2) minimal models is presented. Some examples of N = 1 supersymmetric four dimensional string theories with gauge groups E(6) x (G) over tilde and SO(10) x (N) over tilde are presented, using these minimal models as building blocks. The factor (G) over tilde represents various enhanced symmetry groups made up of products of SU(2) and U(1).