We consider Spin(4)-equivariant dimensional reduction of Yang–Mills theory on manifolds of the form Md×T1,1, where Md is a smooth manifold and T1,1 is a five-dimensional Sasaki–Einstein manifold Spin(4)/U(1). We obtain new quiver gauge theories on Md extending those induced via reduction over the leaf spaces CP1×CP1 in T1,1. We describe the Higgs branches of these quiver gauge theories as moduli spaces of Spin(4)-equivariant instantons on the conifold which is realized as the metric cone over T1,1. We give an explicit construction of these moduli spaces as Kähler quotients.
Geipel, J. C., Lechtenfeld, O., Popov, A. D., & Szabo, R. J. (2016). Sasakian quiver gauge theories and instantons on the conifold. Nuclear Physics B, 907, 445–475. https://doi.org/10.1016/j.nuclphysb.2016.04.016