Hermitian Yang-Mills equations and pseudo-holomorphic bundles on nearly Kahler and nearly Calabi-Yau twistor 6-manifolds

作者：Popov Alexander D^*

来源：Nuclear Physics B, 2010, 828(3): 594-624.

DOI：10.1016/j.nuclphysb.2009.11.011

We consider the Hermitian Yang-Mills (HYM) equations for gauge potentials on a complex vector bundle epsilon over an almost complex manifold X(6) which is the twistor space of an oriented Riemannian manifold M(4). Each solution of the HYM equations on such X(6) defines a pseudo-holomorphic structure on the bundle epsilon. It is shown that the pull-back to X(6) of any anti-self-dual gauge field on M(4) is a solution of the HYM equations on X(6). This correspondence allows us to introduce new twistor actions for bosonic and supersymmetric Yang-Mills theories. As examples of X(6) we consider homogeneous nearly Kahler and nearly Calabi-Yau manifolds which are twistor spaces of S(4), C P(2) and B(4), C B(2) (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.

• 出版日期2010-4-1