Yang-Mills Equations of Motion for the Higgs Sector of SU(3)-Equivariant Quiver Gauge Theories

TL;DR

This paper derives Yang-Mills equations for the Higgs sector in SU(3)-equivariant quiver gauge theories on various spaces, finding specific solutions and highlighting the role of torsion in obtaining non-trivial solutions.

Contribution

It introduces a method to derive equations of motion for Higgs fields in SU(3)-equivariant quiver gauge theories on complex spaces, including solutions with non-zero torsion.

Findings

Non-trivial solutions require specific torsion values.

Derived equations for multiple gauge groups and spaces.

Identified conditions for Higgs field solutions.

Abstract

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on spaces of the form R x SU(3)/H, with H equals either SU(2) x U(1) or U(1) x U(1). For the corresponding quiver gauge theory we derive the equations of motion and construct some specific solutions for the Higgs fields using different gauge groups. Specifically we choose the gauge groups U(6) and U(8) for the space R x CP^2 as well as the gauge group U(3) for the space R x SU(3)/U(1)xU(1), and derive Yang-Mills equations for the latter one using a spin connection endowed with a non-vanishing torsion. We find that a specific value for the torsion is necessary in order to obtain non-trivial solutions of Yang-Mills equations. Finally, we take the space R x CP^1 x CP^2 and derive the equations of motion for the Higgs sector for a U(3m+3) gauge theory.