The existence of K-instantons on a cylinder M 7 = ℝ τ × K/H over a homogeneous nearly Käller 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 ℂ. 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. © 2012 Pleiades Publishing, Ltd.
CITATION STYLE
Lechtenfeld, O. (2012). Instantons and Chern-Simons flows in 6, 7 and 8 dimensions. Physics of Particles and Nuclei, 43(5), 569–576. https://doi.org/10.1134/S1063779612050218
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