Instantons on the exceptional holonomy manifolds of Bryant and Salamon

Abstract

We give a construction of $G_2$ and $Spin(7)$ instantons on exceptional holonomy manifolds constructed by Bryant and Salamon, by using an ansatz of spherical symmetry coming from the manifolds being the total spaces of rank-4 vector bundles. In the $G_2$ case, we show that, in the asymptotically conical model, the connections are asymptotic to Hermitian Yang-Mills connections on the nearly Kähler $S^3\times S^3$.

References in corpus (3)

• Instantons on Special Holonomy Manifolds
• Monopoles on the Bryant-Salamon $G_2$ Manifolds
• Deformation theory of G_2 conifolds

Cited by in corpus (17)

• Monopoles on the Bryant-Salamon $G_2$ Manifolds
• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• $SU(2{)}^2$-invariant $G_2$-instantons
• Deformations of nearly Kähler instantons
• Sigma-model limit of Yang-Mills instantons in higher dimensions
• Generalised Chern-Simons Theory and ${\mathrm{G}}_2$-Instantons over Associative Fibrations
• Gauge theory on Aloff-Wallach spaces
• Instantons on sine-cones over Sasakian manifolds
• Deformations of Asymptotically Conical $G_2$-Instantons
• Deformations of ${\mathrm{G}}_2$-instantons on nearly ${\mathrm{G}}_2$ manifolds
• Deformation Theory of Asymptotically Conical Spin(7)-Instantons
• $G_2$-instantons on noncompact $G_2$-manifolds: results and open problems
• $G_2$-instantons on the spinor bundle of the 3-sphere
• $\mathrm{Spin}(7)$-Instantons from evolution equations
• Warped-like product manifolds with exceptional holonomy groups
• New examples of $G_2$-instantons on ${\mathbb{R}}^4\times S^3$
• Coclosed $G_2$-structures on $\text{SU}(2{)}^2$-invariant cohomogeneity one manifolds