Journal of High Energy Physics

, 2011:103 | Cite as

Yang-Mills instantons on cones and sine-cones over nearly Kähler manifolds

  • Karl-Philip Gemmer
  • Olaf LechtenfeldEmail author
  • Christoph Nölle
  • Alexander D. Popov


We present a unified eight-dimensional approach to instanton equations on several seven-dimensional manifolds associated to a six-dimensional homogeneous nearly Kähler manifold. The cone over the sine-cone on a nearly Kähler manifold has holonomy group Spin(7) and can befoliated by submanifolds with either holonomy group G 2, a nearly parallel G 2-structure or a cocalibrated G 2-structure. We show that there is a G 2-instanton on each of these seven-dimensional manifolds which gives rise to a Spin(7)-instanton in eight dimensions. The well-known octonionic instantons on \( {\mathbb{R}^7} \) and \( {\mathbb{R}^8} \) are contained in our construction as the special cases of an instanton on the cone and on the cone over the sine-cone, both over the six-sphere, respectively.


Flux compactifications Solitons Monopoles and Instantons Differential and Algebraic Geometry 


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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • Karl-Philip Gemmer
    • 1
  • Olaf Lechtenfeld
    • 1
    • 2
    Email author
  • Christoph Nölle
    • 1
  • Alexander D. Popov
    • 3
  1. 1.Institut für Theoretische PhysikLeibniz Universität HannoverHannoverGermany
  2. 2.Centre for Quantum Engineering and Space-Time ResearchLeibniz Universität HannoverHannoverGermany
  3. 3.Bogoliubov Laboratory of Theoretical PhysicsJINRDubnaRussia

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