Seiberg-Witten type monopole equations on 8-manifolds with Spin(7) holonomy as minimizers of a quadratic action

TL;DR

This paper derives elliptic monopole equations on 8-manifolds with Spin(7) holonomy by minimizing a quadratic action involving gauge fields and spinors, extending monopole theory to higher dimensions.

Contribution

It introduces a new set of elliptic monopole equations on Spin(7) manifolds as critical points of a quadratic action, expanding the mathematical framework of gauge theory.

Findings

Derived elliptic monopole equations on Spin(7) manifolds

Established the equations as minimizers of a quadratic action

Extended monopole theory to 8-dimensional manifolds

Abstract

We obtain an elliptic system of monopole equations on 8-manifolds with Spin(7) holonomy by minimizing an action involving negative spinors coupled to an Abelian gauge fields.