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arXiv · 1104.5231

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

Alexander S. Haupt·Tatiana A. Ivanova·Olaf Lechtenfeld·Alexander D. Popov
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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.

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Alexander S. Haupt, Tatiana A. Ivanova, Olaf Lechtenfeld, Alexander D. Popov. 2011-04-27. Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons. https://doi.org/10.1103/physrevd.83.105028

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