Heterotic non-Abelian orbifolds

TL;DR

This paper systematically analyzes particle spectra from heterotic string compactifications on non-Abelian orbifolds, revealing patterns in Hodge numbers and exploring gauge symmetry breaking, with potential implications for string phenomenology.

Contribution

It introduces a new technique for spectrum computation in heterotic orbifolds and provides the first detailed classification of Hodge numbers for non-Abelian orbifold geometries.

Findings

Most Hodge numbers follow h^(1,1) - h^(2,1) = 0 mod 6 pattern.

Identified possibilities for non-local gauge symmetry breaking.

Analyzed specific examples like S_3, T_7, and Δ(27) orbifolds.

Abstract

We perform the first systematic analysis of particle spectra obtained from heterotic string compactifications on non-Abelian toroidal orbifolds. After developing a new technique to compute the particle spectrum in the case of standard embedding based on higher dimensional supersymmetry, we compute the Hodge numbers for all recently classified 331 non-Abelian orbifold geometries which yield N=1 supersymmetry for heterotic compactifications. Surprisingly, most Hodge numbers follow the empiric pattern h^(1,1) - h^(2,1) = 0 mod 6, which might be related to the number of three standard model generations. Furthermore, we study the fundamental groups in order to identify the possibilities for non-local gauge symmetry breaking. Three examples are discussed in detail: the simplest non-Abelian orbifold S_3 and two more elaborate examples, T_7 and \Delta(27), which have only one untwisted Kaehler and no untwisted complex structure modulus. Such models might be especially interesting in the context of no-scale supergravity. Finally, we briefly discuss the case of orbifolds with vanishing Euler numbers in the context of enhanced (spontaneously broken) supersymmetry.