String unification, higher-level gauge symmetries, and exotic hypercharge normalizations

Abstract

We explore the extent to which string theories with higher-level gauge symmetries and nonstandard hypercharge normalizations can reconcile the discrepancy between the string unification scale and the GUT scale extrapolated from the Minimal Supersymmetric Standard Model (MSSM). We determine the phenomenologically allowed regions of ( k y , k 2, k 3) parameter space, and investigate the proposal that there might exist string models with exotic hypercharge normalizations k y which are less than their usual value k y = 5 3 . For a broad class of heterotic string models (encompassing most realistic string models which have been constructed), we prove that k y ⩾ 5 3 . Beyond this class, however, we show that there exist consistent MSSM embeddings which lead to k y < 5 3 . We also consider the constraints imposed on by demanding charge integrality of all unconfined string states, and show that only a limited set of hypercolor confining groups and corresponding values of k y are possible.