Communications in Mathematical Physics

, Volume 300, Issue 1, pp 185–204 | Cite as

Yang-Mills Flows on Nearly Kähler Manifolds and G 2-Instantons

  • Derek HarlandEmail author
  • Tatiana A. Ivanova
  • Olaf Lechtenfeld
  • Alexander D. Popov


We consider Lie(G)-valued G-invariant connections on bundles over spaces \({G/H,\, \mathbb{R}\times G/H\, {\rm and}\, \mathbb{R}^2\times G/H}\), where G/H is a compact nearly Kähler six-dimensional homogeneous space, and the manifolds \({\mathbb{R}\times G/H}\) and \({\mathbb{R}^2\times G/H}\) carry G 2- and Spin(7)-structures, respectively. By making a G-invariant ansatz, Yang-Mills theory with torsion on \({\mathbb{R}\times G/H}\) is reduced to Newtonian mechanics of a particle moving in a plane with a quartic potential. For particular values of the torsion, we find explicit particle trajectories, which obey first-order gradient or hamiltonian flow equations. In two cases, these solutions correspond to anti-self-dual instantons associated with one of two G 2-structures on \({\mathbb{R}\times G/H}\). It is shown that both G 2-instanton equations can be obtained from a single Spin(7)-instanton equation on \({\mathbb{R}^2\times G/H}\).


Manifold Gauge Theory Heterotic String Coset Space Duality Transformation 
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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Derek Harland
    • 1
    Email author
  • Tatiana A. Ivanova
    • 2
  • Olaf Lechtenfeld
    • 1
  • Alexander D. Popov
    • 2
  1. 1.Institut für Theoretische PhysikLeibniz Universität HannoverHannoverGermany
  2. 2.Bogoliubov Laboratory of Theoretical Physics, JINRDubnaRussia

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