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INSTANTONS AND CHERN-SIMONS FLOWS IN SIX AND SEVEN DIMENSIONS // Tomsk State Pedagogical University Bulletin. 2012. Issue 13 (128). P. 103-108

The existence of K-instantons on a cylinder M7 = Rт x K/H over a homogeneous nearly Kahler 6-manifold K/H requires a conformally parallel or a cocalibrated G2-structure on M7. The generalized anti-self-duality onM7 implies a Chern-Simons ow on K/H which runs between instantons on the coset. For K-equivariant connections, the torsionful Yang-Mills equation reduces to a particular quartic dynamics for a Newtonian particle on C. We obtain kink- or bounce-type solutions for generic values of the torsion. When the latter corresponds to the conformally parallel or cocalibrated G2-structure on M7, the dynamics follows from a gradient or hamiltonian ow, respectively, and we encounter Yang-Mills instantons.

Keywords: instantons, Chern-Simons ow, special geometry, G-structures, nearly-Kahler manifolds.