Sasakian quiver gauge theories and instantons on the conifold

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 Kähler quotients.

30 pages

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Cited by in corpus (3)

• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
• Sasakian quiver gauge theory on the Aloff-Wallach space $X_{1,1}$
• Instantons on Calabi-Yau and hyper-Kähler cones