Sasakian quiver gauge theories and instantons on cones over lens 5-spaces

TL;DR

This paper explores new quiver gauge theories derived from SU(3)-equivariant reductions over Sasaki-Einstein manifolds, linking instanton moduli spaces on Calabi-Yau cones to gauge theory structures.

Contribution

It introduces novel quiver gauge theories from reductions over cyclic orbifolds of the 5-sphere and describes their Higgs branches as moduli spaces of instantons on Calabi-Yau cones.

Findings

Higgs branches are described as moduli spaces of SU(3)-equivariant instantons.

Explicit construction of moduli spaces as Kähler quotients.

Moduli spaces share cyclic orbifold singularities with cones over lens 5-spaces.

Abstract

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki-Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki-Einstein structure, which are projective planes. We describe the Higgs branches of these quiver gauge theories as moduli spaces of spherically symmetric instantons which are SU(3)-equivariant solutions to the Hermitian Yang-Mills equations on the associated Calabi-Yau cones, and further compare them to moduli spaces of translationally-invariant instantons on the cones. We provide an explicit unified construction of these moduli spaces as K\"ahler quotients and show that they have the same cyclic orbifold singularities as the cones over the lens 5-spaces.