Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-04-27
Phys.Rev.D83:105028,2011
Physics
High Energy Physics
High Energy Physics - Theory
1+17 pages, 1 figure
Scientific paper
10.1103/PhysRevD.83.105028
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.
Haupt Alexander S.
Ivanova Tatiana A.
Lechtenfeld Olaf
Popov Alexander D.
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