Embedding higher-level Kac-Moody algebras in heterotic string models

Abstract

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 = 1 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. Some explicit examples in four dimensions constructed solely from free, real world-sheet fermions are given, contradicting recent would-be no go theorems, and re-opening 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.