Instantons and the monopole-like equations in eight dimensions

TL;DR

This paper explores an abelian framework for 8-dimensional Yang-Mills instantons on special holonomy manifolds, proposing monopole-like equations inspired by 4D Seiberg-Witten theory and testing a form of S-duality.

Contribution

It introduces a novel set of monopole-like equations for 8D instantons, extending ideas from 4D Seiberg-Witten theory to higher dimensions.

Findings

Proposes monopole-like equations for 8D instantons

Tests generalized S-duality in 8D Yang-Mills theory

Identifies challenges in the abelian description approach

Abstract

We search for an abelian description of the Yang-Mills instantons on certain eight dimensional manifolds with the special holonomies $Spin(7)$ and SU(4). By mimicing the Seiberg-Witten theory in four dimensions, we propose a set of monopole-like equations governing the 8-dimensional U(1) connections and spinors, which are supposed to be the dual theory of the nonabelian instantons. We also give a naive test of the generalized $S$-duality in the abelian sector of 8-dimensional Yang-Mills theory. Some problems in this approach are pointed out.