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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
Article

Abstract

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 \({\mathbb{R}^2\times G/H}\).

Keywords

Manifold Gauge Theory Heterotic String Coset Space Duality Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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