Sasakian quiver gauge theories and instantons on the conifold

TL;DR

This paper explores the reduction of Yang-Mills theory on manifolds involving the Sasaki-Einstein space T^{1,1}, leading to new quiver gauge theories and describing their Higgs branches as moduli spaces of instantons on the conifold.

Contribution

It introduces new quiver gauge theories from dimensional reduction over T^{1,1} and characterizes their Higgs branches as moduli spaces of equivariant instantons on the conifold.

Findings

Derived new quiver gauge theories on M^d.

Described Higgs branches as moduli spaces of instantons.

Constructed moduli spaces explicitly as Kähler quotients.

Abstract

We consider Spin(4)-equivariant dimensional reduction of Yang-Mills theory on manifolds of the form $M^d \times T^{1,1}$, where $M^d$ is a smooth manifold and $T^{1,1}$ is a five-dimensional Sasaki-Einstein manifold Spin(4)/U(1). We obtain new quiver gauge theories on $M^d$ extending those induced via reduction over the leaf spaces $\mathbb{C}P^1 \times \mathbb{C}P^1$ in $T^{1,1}$. 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 $T^{1,1}$. We give an explicit construction of these moduli spaces as K\"ahler quotients.