# Hermitian-Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds - High Energy Physics - Theory

Hermitian-Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds - High Energy Physics - Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: We consider the Hermitian-Yang-Mills HYM equations for gauge potentials ona complex vector bundle E over an almost complex manifold X^6 which is thetwistor space of an oriented Riemannian manifold M^4. Each solution of the HYMequations on such X^6 defines a pseudo-holomorphic structure on the bundle E.It is shown that the pull-back to X^6 of any anti-self-dual gauge field on M^4is a solution of the HYM equations on X^6. This correspondence allows us tointroduce new twistor actions for bosonic and supersymmetric Yang-Millstheories. As examples of X^6 we consider homogeneous nearly Kaehler and nearlyCalabi-Yau manifolds which are twistor spaces of S^4, CP^2 and B 4, CB 2 real4-ball and complex 2-ball, respectively. Various explicit examples ofsolutions to the HYM equations on these spaces are provided. Applications influx compactifications of heterotic strings are briefly discussed.

Author: ** Alexander D. Popov**

Source: https://arxiv.org/