String Unification, Higher-Level Gauge Symmetries, and Exotic Hypercharge Normalizations

TL;DR

This paper investigates how string theories with higher-level gauge symmetries and non-standard hypercharge normalizations can address the mismatch between string and GUT unification scales, identifying allowed parameter regions and constraints.

Contribution

It demonstrates that for most realistic heterotic string models, hypercharge normalization k_Y is at least 5/3, but exceptions exist outside this class, with implications for model building.

Findings

Most realistic models have k_Y >= 5/3

Existence of models with k_Y < 5/3 outside the typical class

Charge integrality constraints limit hypercolor confining groups

Abstract

We explore the extent to which string theories with higher-level gauge symmetries and non-standard 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 k_Y 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.