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

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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.

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References

  1. K.-P. Gemmer and O. Lechtenfeld, C. Nölle, and A. D. Popov, J. High Energy Phys. 09, 103 (2011). arXiv:1108.3951

    Article  ADS  Google Scholar 

  2. D. Harland, T. A. Ivanova, O. Lechtenfeld, and A. D. Popov, Commun. Math. Phys. 300, 185 (2010). arXiv:0909.2730

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. I. Bauer, T. A. Ivanova, O. Lechtenfeld, and F. Lubbe, J. High Energy Phys. 10, 44 (2010). arXiv:1006.2388

    Article  MathSciNet  ADS  Google Scholar 

  4. O. Lechtenfeld, C. Nölle, and A. D. Popov, J. High Energy Phys. 09, 074 (2010). arXiv:1007.0236

    Article  ADS  Google Scholar 

  5. A. Chatzistavrakidis, O. Lechtenfeld, and A. D. Popov, High Energy Phys. 4, 114 (2012). arXiv:1202.1278.

    Article  ADS  Google Scholar 

  6. K.-P. Gemmer, A. Haupt, O. Lechtenfeld, C. Nölle, and A. D. Popov, arXiv:1202.5046.

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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

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  • DOI: https://doi.org/10.1134/S1063779612050218

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