Gauge symmetry breaking in orbifold model building

TL;DR

This paper reviews a non-local gauge symmetry breaking mechanism in orbifold models, emphasizing its relation to compactification moduli and its distinction from traditional Higgs or Hosotani mechanisms.

Contribution

It demonstrates the existence of a scale of symmetry breaking linked to moduli in non-local orbifold projections, differing from localized breaking in standard models.

Findings

Breaking scale is related to compactification moduli.

Non-local breaking differs from Higgs and Hosotani mechanisms.

Applicable to heterotic and open string compactifications.

Abstract

We review the gauge symmetry breaking mechanism due to orbifold projections in orbifold model building. We explicitly show the existence of a scale of breaking if such a symmetry breaking is due to freely-acting orbifold operators only, i.e. in case the breaking is realized non-locally in the internal space. We show that such a scale is related to the compactification moduli only, and that there are no extra continuous parameters, at least in semirealistic models with N=1 SUSY in four dimensions. In this sense, the mechanism is peculiarly different from the standard Higgs (or Hosotani) symmetry breaking mechanism. We show that the mechanism also differs from that present in standard orbifold models where, even in presence of discrete Wilson lines, a scale of breaking is generically missing, since the breaking is localized in specific points in the internal space. We review a set of background geometries where the described non-local breaking is realized, both in the case of two and six extra dimensions. In the latter case, relevant in string model building, we consider both heterotic and open string compactifications.