Aloff-Wallach空间上的Chern-Simons流和自旋（7）瞬子
Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons
摘要：
由于它们的显式构造，Aloff-Wallach空间在通量紧化中是突出的。它们具有G_2-结构，并承认G_2-瞬子方程，这是七维流形上Yang-Mills瞬子的自然BPS方程，极值化了一个Chern-Simons型泛函。考虑Aloff-Wallach空间上不同G_2-瞬子之间的Chern-Simons流，它等价于Aloff-Wallach空间上圆柱上的Spin（7）-瞬子.对于一般的SU（3）-等变规范连接，广义瞬子方程转化为具有特定立方超势的C^3 x R^2上的梯度流方程。对于最简单的Aloff-Wallach家族成员（具有3-Sasakian结构），我们提出了一个明确的双曲正切形状的瞬子解。
英文摘要：
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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