Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons

Abstract

We consider a complex vector bundle E endowed with a connection A over the eight-dimensional manifold R^2 x G/H, where G/H = SU(3)/U(1)xU(1) is a homogeneous space provided with a never integrable almost complex structure and a family of SU(3)-structures. We establish an equivalence between G-invariant solutions A of the Spin(7)-instanton equations on R^2 x G/H and general solutions of non-Abelian coupled vortex equations on R^2. These vortices are BPS solitons in a d=4 gauge theory obtained from N=1 supersymmetric Yang-Mills theory in ten dimensions compactified on the coset space G/H with an SU(3)-structure. The novelty of the obtained vortex equations lies in the fact that Higgs fields, defining morphisms of vector bundles over R^2, are not holomorphic in the generic case. Finally, we introduce BPS vortex equations in N=4 super Yang-Mills theory and show that they have the same feature.

14 pages; v2: typos fixed, published version

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Cited by in corpus (12)

• Yang-Mills flows on nearly Kaehler manifolds and G_2-instantons
• Yang-Mills instantons and dyons on homogeneous G_2-manifolds
• Double quiver gauge theory and nearly Kahler flux compactifications
• Instantons on Special Holonomy Manifolds
• Integrable vortex-type equations on the two-sphere
• Contact Manifolds, Contact Instantons, and Twistor Geometry
• Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons
• Deformations of nearly Kähler instantons
• Yang-Mills fields in flux compactifications on homogeneous manifolds with SU(4)-structure
• Instantons in six dimensions and twistors
• Instantons on the six-sphere and twistors
• Instantons, five-branes and fractional strings