Instantons and Yang–Mills Flows on Coset Spaces

  • Tatiana A. IvanovaEmail author
  • Olaf Lechtenfeld
  • Alexander D. Popov
  • Thorsten Rahn


We consider the Yang–Mills flow equations on a reductive coset space G/H and the Yang–Mills equations on the manifold \({\mathbb{R}\times G/H}\). On non-symmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang–Mills equations to \({\phi^4}\)-kink equations on \({\mathbb{R}}\). Depending on the boundary conditions and torsion, we obtain solutions to the Yang–Mills equations describing instantons, chains of instanton–anti-instanton pairs or modifications of gauge bundles. For Lorentzian signature on \({\mathbb{R}\times G/H}\), dyon-type configurations are constructed as well. We also present explicit solutions to the Yang–Mills flow equations and compare them with the Yang–Mills solutions on \({\mathbb{R}\times G/H}\).

Mathematics Subject Classification (2000)

81T13 83E15 


Yang-Mills instantons kinks flows 


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Copyright information

© Springer 2009

Authors and Affiliations

  • Tatiana A. Ivanova
    • 1
    Email author
  • Olaf Lechtenfeld
    • 2
  • Alexander D. Popov
    • 1
  • Thorsten Rahn
    • 2
  1. 1.Bogoliubov Laboratory of Theoretical Physics, JINRMoscow RegionRussia
  2. 2.Institut für Theoretische PhysikLeibniz Universität HannoverHannoverGermany

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