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Yang-Mills instantons and dyons on homogeneous G 2-manifolds

  • Irina Bauer
  • Tatiana A. Ivanova
  • Olaf Lechtenfeld
  • Felix Lubbe
Article

Abstract

We consider LieG-valued Yang-Mills fields on the space \( \mathbb{R} \times {{G} \left/ {H} \right.} \), where G/H is a compact nearly Kähler six-dimensional homogeneous space, and the manifold \( \mathbb{R} \times {{G} \left/ {H} \right.} \) carries a G 2-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on \( \mathbb{R} \times {{G} \left/ {H} \right.} \) is reduced to Newtonian mechanics of a particle moving in \( {\mathbb{R}^6} \), \( {\mathbb{R}^4} \) or \( {\mathbb{R}^2} \) under the influence of an inverted double-well-type potential for the cases G/H = SU(3)/ U(1)×U(1), Sp(2)/ Sp(1)×U(1) or G2/SU(3), respectively. We analyze all critical points and present analytical and numerical kink-and bounce-type solutions, which yield G-invariant instanton configurations on those cosets. Periodic solutions on S 1×G/H and dyons on \( i\mathbb{R} \times {{G} \left/ {H} \right.} \) are also given.

Keywords

Flux compactifications Solitons Monopoles and Instantons Differential and Algebraic Geometry 

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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Irina Bauer
    • 1
  • Tatiana A. Ivanova
    • 3
  • Olaf Lechtenfeld
    • 1
    • 2
  • Felix Lubbe
    • 1
  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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