Voisin-Borcea Manifolds and Heterotic Orbifold Models

TL;DR

This paper explores the connection between heterotic orbifold models and smooth Voisin-Borcea Calabi-Yau compactifications, analyzing moduli, gauge groups, and spectra to understand their relationships and differences.

Contribution

It provides a detailed geometric and gauge-theoretic analysis linking heterotic orbifold models to Voisin-Borcea Calabi-Yau compactifications, including moduli matching and spectrum behavior.

Findings

The orbifold model's twisted states correspond to geometric moduli.

Higgsing alters the gauge group, losing the standard model subgroup.

Post-higgsing spectrum becomes non-chiral under the remaining gauge group.

Abstract

We study the relation between a heterotic T^6/Z6 orbifold model and a compactification on a smooth Voisin-Borcea Calabi-Yau three-fold with non-trivial line bundles. This orbifold can be seen as a Z2 quotient of T^4/Z3 x T^2. We consider a two-step resolution, whose intermediate step is (K3 x T^2)/Z2. This allows us to identify the massless twisted states which correspond to the geometric Kaehler and complex structure moduli. We work out the match of the two models when non-zero expectation values are given to all twisted geometric moduli. We find that even though the orbifold gauge group contains an SO(10) factor, a possible GUT group, the subgroup after higgsing does not even include the standard model gauge group. Moreover, after higgsing, the massless spectrum is non-chiral under the surviving gauge group.