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 G2-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 Spin(7)-instantons on R8, where R8 is considered to be an asymptotically conical Spin(7)-manifold asymptotic to the cone over S7. We calculate the virtual dimension of the moduli space using Atiyah–Patodi–Singer index theorem and the spectrum of the twisted Dirac operator.