Gauge Symmetry Breaking in Flux Compactification with Wilson-line Scalar Condensate

TL;DR

This paper investigates how gauge symmetry can be broken in six-dimensional flux compactifications by analyzing the one-loop effective potential influenced by Wilson-line scalar condensates, demonstrating symmetry breaking in SU(2) and SU(3) models.

Contribution

It reveals that a non-zero VEV of scalar fields induces gauge symmetry breaking through the one-loop effective potential in flux compactified theories.

Findings

The one-loop effective potential is generated by non-zero VEV effects.

The potential minimum occurs at non-zero VEVs, leading to symmetry breaking.

Gauge symmetry is broken in SU(2) and SU(3) models due to these effects.

Abstract

We discuss the gauge symmetry breaking of six dimensional theories in flux compactification with a magnetic flux background and a constant vacuum expectation value (VEV) for the scalar fields, which are zero modes of extra spatial components of the gauge field. Although the effective potential for the scalar fields are known not to be generated classically and radiatively in a magnetic flux background only, the one-loop effective potential is shown to be generated by the effects of the non-zero constant VEV. As illustrations, we calculate the one-loop effective potential in SU(2) and SU(3) Yang-Mills theories. In both cases, we find that the potential minimum is located at non-zero VEV and the gauge symmetry breaking takes place.