A Review of Three-Family Grand Unified String Models

TL;DR

This paper reviews three-family grand unified string models constructed via asymmetric orbifolds, analyzing their superpotentials, phenomenological issues like proton stability, Yukawa matrices, and supersymmetry breaking, highlighting challenges in achieving realistic models.

Contribution

It provides a comprehensive survey of three-family GUT string models, computes their superpotentials, and examines phenomenological and supersymmetry breaking aspects, revealing limitations in current models.

Findings

Models require fine-tuning for phenomenological viability.

Supersymmetry breaking scales are incompatible with the electroweak hierarchy.

None of the models fully resolve phenomenological challenges.

Abstract

We review the construction and classification of three-family grand unified models within the framework of asymmetric orbifolds in perturbative heterotic superstring. We give a detailed survey of all such models which is organized to aid analysis of their phenomenological properties. We compute tree-level superpotentials for these models. These superpotentials are used to analyze the issues of proton stability (doublet-triplet splitting and R-parity violating terms) and Yukawa mass matrices. To have agreement with phenomenological data all these models seem to require certain degree of fine-tuning. We also analyze the possible patterns of supersymmetry breaking in these models. We find that the supersymmetry breaking scale comes out either too high to explain the electroweak hierarchy problem, or below the electroweak scale unless some degree of fine-tuning is involved. Thus, none of the models at hand seem to be phenomenologically flawless.