Orientability of the moduli space of Spin(7)-instantons

TL;DR

This paper proves that under certain topological conditions, the moduli space of irreducible Spin(7)-instantons on an 8-manifold is orientable, advancing understanding of gauge theory in higher dimensions.

Contribution

It establishes the orientability of the moduli space of Spin(7)-instantons under specific topological constraints, a novel result in higher-dimensional gauge theory.

Findings

Moduli space of Spin(7)-instantons is orientable when Hom(H^3(M,Z),Z_2)=0.

Provides conditions for orientability in 8-dimensional gauge theory.

Advances understanding of geometric structures on manifolds with Spin(7)-structure.

Abstract

Let $(M,\Omega)$ be a closed $8$-dimensional manifold equipped with a generically non-integrable $\mathrm{Spin}(7)$-structure $\Omega$. We prove that if $\mathrm{Hom}(H^{3}(M,\mathbb{Z}), \mathbb{Z}_{2}) = 0$ then the moduli space of irreducible $\mathrm{Spin}(7)$-instantons on $(M,\Omega)$ with gauge group $\mathrm{SU}(r)$, $r\geq 2$, is orientable.