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.
Keywords
Cite
@article{arxiv.1104.5231,
title = {Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons},
author = {Alexander S. Haupt and Tatiana A. Ivanova and Olaf Lechtenfeld and Alexander D. Popov},
journal= {arXiv preprint arXiv:1104.5231},
year = {2011}
}
Comments
1+17 pages, 1 figure