Heterotic Brane World

TL;DR

This paper argues that heterotic string theory on orbifolds provides a concrete, calculable route to chiral 4D theories with realistic gauge structures. By embedding point-group twists into gauge degrees of freedom and using Wilson lines, the authors show how gauge breaking, family replication, and matter localization can be engineered in a brane-world picture, including Z$_N$ and Z$_N\times$Z$_M$ constructions with rich spectra. They demonstrate the geometric interpretation of bulk versus brane fields, discuss gauge-group geography at fixed points, and present toy models (e.g., SO(10) with three families) that illustrate the potential to realize the Standard Model with GUT remnants, while outlining the remaining challenges such as rank reduction and hypercharge embedding. The work lays out a framework for systematic model-building and connects string constructions to orbifold GUT concepts, with implications for gauge coupling unification, Yukawa textures, and proton stability.

Abstract

Orbifold compactification of heterotic E8 x E8 string theory is a source for promising grand unified model building. It can accommodate the successful aspects of grand unification while avoiding problems like doublet-triplet splitting in the Higgs sector. Many of the phenomenological properties of the 4-dimensional effective theory find an explanation through the geometry of compact space and the location of matter and Higgs fields. These geometrical properties can be used as a guideline for realistic model building.

Figures (11)

• Figure 1: ${\mathbb Z}_3$ orbifold. The circle, triangle, and square denote the fixed points.
• Figure 2: ${\mathbb Z}_3$ orbifold with non-vanishing Wilson lines $A_1, A_2$. The circles around the fixed points indicate that the degeneracy in the first torus is lifted.
• Figure 3: Action of the twists in the case of the ${\mathbb Z}_2\times {\mathbb Z}_2$ orbifold. The crosses indicate the fixed points.
• Figure 4: Intersecting brane picture: The picture shows one brane of each twisted sector. The intersection is $4d$ Minkowski space. The branes are mutually orthogonal in the six compact dimensions.
• Figure 5: Wilson line in $e_3$ direction lifts the degeneracy of the fixed points as indicated by the boxes.