Generalised Chern-Simons Theory and ${\mathrm{G}}_2$-Instantons over Associative Fibrations

Abstract

Adjusting conventional Chern-Simons theory to ${\mathrm{G}}_2$-manifolds, one describes ${\mathrm{G}}_2$-instantons on bundles over a certain class of $7$-dimensional flat tori which fiber non-trivially over $T^4$, by a pullback argument. Moreover, if $c_2\ne 0$, any (generic) deformation of the ${\mathrm{G}}_2$-structure away from such a fibred structure causes all instantons to vanish. A brief investigation in the general context of (conformally compatible) associative fibrations $f:Y^7\to X^4$ relates ${\mathrm{G}}_2$-instantons on pullback bundles $f^{\ast }E\to Y$ and self-dual connections on the bundle $E\to X$ over the base, a fact which may be of independent interest.

references updated

Cited by in corpus (9)

• The infinitesimal moduli space of heterotic $G_2$ systems
• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• Deformations of nearly Kähler instantons
• Sigma-model limit of Yang-Mills instantons in higher dimensions
• Instantons on Sasakian 7-manifolds
• Current progress on $G_2$--instantons over twisted connected sums
• Asymptotic behaviour of instantons on Cylinder Manifolds
• The Structure Constants of the Exceptional Lie Algebra ${\mathfrak{g}}_2$ in the Cartan-Weyl Basis
• Instantons on Cylindrical Manifolds