Instantons and Chern-Simons flows in 6, 7 and 8 dimensions

The existence of K-instantons on a cylinder M-7 = a"e(tau) x K/H over a homogeneous nearly Kaller 6-manifold K/H requires a conformally parallel or a cocalibrated G (2)-structure on M (7). The generalized anti-self-duality on M (7) implies a Chern-Simons flow 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 a",. When the torsion corresponds to one of the G (2)-structures, this dynamics follows from a gradient or hamiltonian flow equation, respectively. We present the analytic (kink-type) solutions and plot numerical non-BPS solutions for general torsion values interpolating between the instantonic ones.