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

摘要

The existence of K-instantons on a cylinder M ~7 = ? _τ × K/H over a homogeneous nearly K?ller 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 ?. 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.