Instantons on sine-cones over Sasakian manifolds

Abstract

We investigate instantons on sine-cones over Sasaki-Einstein and 3-Sasakian manifolds. It is shown that these conical Einstein manifolds are K"ahler with torsion (KT) manifolds admitting Hermitian connections with totally antisymmetric torsion. Furthermore, a deformation of the metric on the sine-cone over 3-Sasakian manifolds allows one to introduce a hyper-K"ahler with torsion (HKT) structure. In the large-volume limit these KT and HKT spaces become Calabi-Yau and hyper-K"ahler conifolds, respectively. We construct gauge connections on complex vector bundles over conical KT and HKT manifolds which solve the instanton equations for Yang-Mills fields in higher dimensions.

arXiv comment1+15 pages, 2 figures

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• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• Sigma-model limit of Yang-Mills instantons in higher dimensions
• Sasakian quiver gauge theories and instantons on the conifold
• Instantons on Calabi-Yau cones
• Sasakian quiver gauge theory on the Aloff-Wallach space $X_{1,1}$
• Spectra, rigidity and stability of sine-cones