Gepner's theory of compactified strings

Abstract

Space time supersymmetric compactified string theories which obey the modular invariance, the correct spin-statistics and the absence of tachyons, are constructed by taking for the internal space the arbitrary sums of N=2 minimal superconformal models. There exist 168 kinds of compactifications to the four dimensional space-time. Superstring compactifications have too small gauge groups, but heterotic ones large gauge groups which contain E6 with chiral fermions in the realistic grand unification theories. We also find the partition functions and modular invariants for the parafermionic theories and the N = 2 minimal superconformal models.