Equivalence Classes of Boundary Conditions in Gauge Theory on $Z_3$ Orbifold

TL;DR

This paper investigates boundary condition classes in gauge theories on a $Z_3$ orbifold, analyzing gauge equivalences via the Hosotani mechanism and computing the one-loop effective potential for Wilson line phases.

Contribution

It introduces a classification of boundary condition equivalence classes on a $Z_3$ orbifold and calculates the one-loop effective potential for Wilson lines in this setting.

Findings

Classification of boundary condition equivalence classes.

Explicit mode expansions for $Z_3$ singlet and triplet fields.

Calculation of the one-loop effective potential for Wilson line phases.

Abstract

We study equivalence classes of boundary conditions in gauge theory on the orbifold $T^2/Z_3$. Orbifold conditions and those gauge transformation properties are given and the gauge equivalence is understood by the Hosotani mechanism. Mode expansions are carried out for six-dimensional $Z_3$ singlet fields and a $Z_3$ triplet field, and the one-loop effective potential for Wilson line phases is calculated.