Deformation Theory of Asymptotically Conical Spin(7)-Instantons

Abstract

We develop the deformation theory of instantons on asymptotically conical $Spin(7)$-manifolds where the instanton is asymptotic to a fixed nearly $G_2$-instanton at infinity. By relating the deformation complex with spinors, we identify the space of infinitesimal deformations with the kernel of the twisted negative Dirac operator on the asymptotically conical $Spin(7)$-manifold. Finally we apply this theory to describe the deformations of Fairlie-Nuyts-Fubini-Nicolai (FNFN) $Spin(7)$-instantons on ${\mathbb{R}}^8$, where ${\mathbb{R}}^8$ is considered to be an asymptotically conical $Spin(7)$-manifold asymptotic to the cone over $S^7$. We calculate the virtual dimension of the moduli space using Atiyah-Patodi-Singer index theorem and the spectrum of the twisted Dirac operator.

30 pages. A shortened version for publication

References in corpus (9)

• Flows of G_2 Structures, I
• Yang-Mills flows on nearly Kaehler manifolds and G_2-instantons
• Instantons on the exceptional holonomy manifolds of Bryant and Salamon
• Monopoles on the Bryant-Salamon $G_2$ Manifolds
• Deformation theory of G_2 conifolds
• $SU(2{)}^2$-invariant $G_2$-instantons
• A construction of Spin(7)-instantons
• Deformations of nearly Kähler instantons
• Complete non-compact Spin(7) manifolds from self-dual Einstein 4-orbifolds