Hermitian Yang–Mills equations and pseudo-holomorphic bundles on nearly Kähler and nearly Calabi–Yau twistor 6-manifolds Original Research Article

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