Stable Yang-Mills connections on Special Holonomy Manifolds

Abstract

We prove that energy minimizing Yang-Mills connections on a compact $G_2$-manifold has holonomy equal to $G_2$ are $G_2$-instantons, subject to an extra condition on the curvature. Furthermore, we show that energy minimizing connections on a compact Calabi-Yau $3$-fold has holonomy equal to $SU(3)$ subject to a similar condition are holomorphic.

Final Version; will be appear in JGP. arXiv admin note: text overlap with arXiv:0808.0667 by other authors

References in corpus (2)

• Gauge Theory in higher dimensions, II
• Manifolds with parallel differential forms and Kaehler identities for G_2-manifolds