Abstract
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.
Similar content being viewed by others
References
K.-P. Gemmer and O. Lechtenfeld, C. Nölle, and A. D. Popov, J. High Energy Phys. 09, 103 (2011). arXiv:1108.3951
D. Harland, T. A. Ivanova, O. Lechtenfeld, and A. D. Popov, Commun. Math. Phys. 300, 185 (2010). arXiv:0909.2730
I. Bauer, T. A. Ivanova, O. Lechtenfeld, and F. Lubbe, J. High Energy Phys. 10, 44 (2010). arXiv:1006.2388
O. Lechtenfeld, C. Nölle, and A. D. Popov, J. High Energy Phys. 09, 074 (2010). arXiv:1007.0236
A. Chatzistavrakidis, O. Lechtenfeld, and A. D. Popov, High Energy Phys. 4, 114 (2012). arXiv:1202.1278.
K.-P. Gemmer, A. Haupt, O. Lechtenfeld, C. Nölle, and A. D. Popov, arXiv:1202.5046.
Author information
Authors and Affiliations
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Lechtenfeld, O. Instantons and Chern-Simons flows in 6, 7 and 8 dimensions. Phys. Part. Nuclei 43, 569–576 (2012). https://doi.org/10.1134/S1063779612050218
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063779612050218