Hermitian Yang-Mills equations and pseudo-holomorphic bundles on nearly Kähler and nearly Calabi-Yau twistor 6-manifolds
Abstract
We consider the Hermitian Yang-Mills (HYM) equations for gauge potentials on a complex vector bundle E over an almost complex manifold X which is the twistor space of an oriented Riemannian manifold M. Each solution of the HYM equations on such X defines a pseudo-holomorphic structure on the bundle E. It is shown that the pull-back to X of any anti-self-dual gauge field on M is a solution of the HYM equations on X. This correspondence allows us to introduce new twistor actions for bosonic and supersymmetric Yang-Mills theories. As examples of X we consider homogeneous nearly Kähler and nearly Calabi-Yau manifolds which are twistor spaces of S, CP and B, CB (real 4-ball and complex 2-ball), respectively. Various explicit examples of solutions to the HYM equations on these spaces are provided. Applications in flux compactifications of heterotic strings are briefly discussed.
- Publication:
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Nuclear Physics B
- Pub Date:
- April 2010
- DOI:
- 10.1016/j.nuclphysb.2009.11.011
- arXiv:
- arXiv:0907.0106
- Bibcode:
- 2010NuPhB.828..594P
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 31 pages