Transversality for the moduli space of Spin(7)-instantons

TL;DR

This paper constructs and analyzes the moduli space of Spin(7)-instantons on 8-dimensional manifolds, establishing conditions for smoothness and expected dimension through perturbations, advancing understanding of gauge theory in higher dimensions.

Contribution

It introduces a method to achieve regularity of the Spin(7)-instanton moduli space via perturbations, even on non-integrable structures, and characterizes its smoothness and dimension.

Findings

Moduli space of Spin(7)-instantons can be made smooth with suitable perturbations.

The dimension of the moduli space matches the expected dimension.

Regularity is achieved over the irreducible locus.

Abstract

We construct the moduli space of Spin(7)-instantons on a hermitian complex vector bundle over a closed 8-dimensional manifold endowed with a (possibly non-integrable) Spin(7)-structure. We find suitable perturbations that achieve regularity of the moduli space, so that it is smooth and of the expected dimension over the irreducible locus.