Instantons and Chern-Simons flows in 6, 7 and 8 dimensions
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The existence of K-instantons on a cylinder M7 = ℝτ × 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.
KeywordsManifold High Energy Phys Coset Space Duality Condition Mill Equation
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- 6.K.-P. Gemmer, A. Haupt, O. Lechtenfeld, C. Nölle, and A. D. Popov, arXiv:1202.5046.Google Scholar