2016/05/11 by Jakob C. Geipel
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Black Holes and Theoretical Physics #Equivariant map #Gauge theory #Geometry and complex manifolds #Instanton #Manifold (fluid mechanics) #Mathematical physics #Mathematics #Moduli space #Physics #Pure mathematics #Quiver #Space (punctuation) #Vector bundle #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2017.01.006
25 pages
arxiv created 2016/05/11 · openalex publication_date 2017/01/11 · arxiv updated 2017/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the SU ( 3 ) -equivariant dimensional reduction of gauge theories on spaces of the form M d × X 1 , 1 with d -dimensional Riemannian manifold M d and the Aloff–Wallach space X 1 , 1 = SU ( 3 ) / U ( 1 ) endowed with its Sasaki–Einstein structure. The condition of SU ( 3 ) -equivariance of vector bundles, which has already occurred in the studies of Spin ( 7 ) -instantons on cones over Aloff–Wallach spaces, is interpreted in terms of quiver diagrams, and we construct the corresponding quiver bundles, using (parts of) the weight diagram of SU ( 3 ) . We consider three examples thereof explicitly and then compare the results with the quiver gauge theory on Q 3 = SU ( 3 ) / ( U ( 1 ) × U ( 1 ) ) , the leaf space underlying the Sasaki–Einstein manifold X 1 , 1 . Moreover, we study instanton solutions on the metric cone C ( X 1 , 1 ) by evaluating the Hermitian Yang–Mills equation. We briefly discuss some features of the moduli space thereof, following the main ideas of a treatment of Hermitian Yang–Mills instantons on cones over generic Sasaki–Einstein manifolds in the literature.