Hermitian YangMills equations and pseudoholomorphic bundles on nearly Kähler and nearly CalabiYau twistor 6manifolds
Abstract
We consider the Hermitian YangMills (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 pseudoholomorphic structure on the bundle E. It is shown that the pullback to X of any antiselfdual 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 YangMills theories. As examples of X we consider homogeneous nearly Kähler and nearly CalabiYau manifolds which are twistor spaces of S, CP and B, CB (real 4ball and complex 2ball), 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:

Nuclear Physics B
 Pub Date:
 April 2010
 DOI:
 10.1016/j.nuclphysb.2009.11.011
 arXiv:
 arXiv:0907.0106
 Bibcode:
 2010NuPhB.828..594P
 Keywords:

 High Energy Physics  Theory
 EPrint:
 31 pages