Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons

Abstract

Due to their explicit construction, Aloff-Wallach spaces are prominent in flux compactifications. They carry G_2-structures and admit the G_2-instanton equations, which are natural BPS equations for Yang-Mills instantons on seven-manifolds and extremize a Chern-Simons-type functional. We consider the Chern-Simons flow between different G_2-instantons on Aloff-Wallach spaces, which is equivalent to Spin(7)-instantons on a cylinder over them. For a general SU(3)-equivariant gauge connection, the generalized instanton equations turn into gradient-flow equations on C^3 x R^2, with a particular cubic superpotential. For the simplest member of the Aloff-Wallach family (with 3-Sasakian structure) we present an explicit instanton solution of tanh-like shape.

1+17 pages, 1 figure

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Cited by in corpus (11)

• Instantons and Killing spinors
• Instantons on Special Holonomy Manifolds
• Contact Manifolds, Contact Instantons, and Twistor Geometry
• Deformations of nearly Kähler instantons
• Instantons on sine-cones over Sasakian manifolds
• Gauge theory on Aloff-Wallach spaces
• Instantons on Calabi-Yau cones
• Sasakian quiver gauge theory on the Aloff-Wallach space $X_{1,1}$
• Instantons, five-branes and fractional strings
• Cho decomposition, Abelian gauge fixing and monopoles in G(2) Yang-Mills theory
• Yang-Mills Solutions and Dyons on Cylinders over Coset Spaces with Sasakian Structure