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

Understand

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.