Sasakian quiver gauge theories and instantons on the conifold

We consider Spin(4)Spin(4)-equivariant dimensional reduction of Yang–Mills theory on manifolds of the form Md×T1,1Md×T1,1, where MdMd is a smooth manifold and T1,1T1,1 is a five-dimensional Sasaki–Einstein manifold Spin(4)/U(1)Spin(4)/U(1). We obtain new quiver gauge theories on MdMd extending those induced via reduction over the leaf spaces CP1×CP1CP1×CP1 in T1,1T1,1. We describe the Higgs branches of these quiver gauge theories as moduli spaces of Spin(4)Spin(4)-equivariant instantons on the conifold which is realized as the metric cone over T1,1T1,1. We give an explicit construction of these moduli spaces as Kähler quotients.