Embedding Higher Level Kac - Moody Algebras in Heterotic String Models

Heterotic string models in which the space-time gauge symmetry is realized as a level k > 2 Kac-Moody algebra on the string world-sheet offer phenomenological features not present for the level k = 1 case (which includes all heterotic string models seriously considered to date). In particular, string models with N=l space-time supersymmetry and/or chiral matter fields can contain massless scalar fields in the adjoint (or higher dimensional) representation of the gauge group provided that k 2 2. Some explicit examples in four dimensions constructed solely from free, real world-sheet-fermions are given, contradicting recent would-be no go theorems, and reopening the possibilities for embedding standard Grand Unified Theories within string models. The possibilities for more general constructions allowing higher level Kac-Moody algebras are also briefly discussed.