Geometry of Rank Reduction

TL;DR

This paper presents a geometric approach to gauge symmetry reduction in string theory using continuous Wilson lines, linking orbifold twists to Higgs mechanisms for smooth symmetry breaking.

Contribution

It introduces continuous Wilson lines for rank reduction in orbifold models and provides a geometric interpretation of symmetry breaking as a Higgs mechanism.

Findings

Provides a geometric picture of gauge symmetry reduction

Shows the embedding into heterotic string theory

Describes smooth symmetry breaking via Wilson lines

Abstract

We introduce continuous Wilson lines to reduce the rank of the gauge group in orbifold constructions. In situations where the orbifold twist can be realised as a rotation in the root lattice of a grand unified group we derive an appealing geometric picture of the symmetry breakdown. This symmetry breakdown is smooth and corresponds to a standard field theory Higgs mechanism. The embedding into heterotic string theory is discussed.