Yang-Mills fields in flux compactifications on homogeneous manifolds with SU(4)-structure

TL;DR

This paper investigates SU(4)-instanton equations on specific 8-manifolds with flux, reducing them to simpler equations on lower-dimensional spaces, and provides explicit solutions where possible.

Contribution

It introduces a G-invariant reduction of SU(4)-instanton equations on flux compactifications, connecting to geometric Langlands and providing explicit solutions.

Findings

Reduction of instanton equations to lower-dimensional manifolds

Identification of equations related to geometric Langlands program

Explicit solutions in certain examples

Abstract

The SU(4)-instanton equations are natural BPS equations for instantons on 8-manifolds. We study these equations on nearly Kaehler and Calabi-Yau torsion manifolds of the form M x G/H, with G/H a coset space and M a product of a torus with Euclidean space. By imposing G-invariance the instanton equations reduce to interesting equations on M; for example, equations used by Kapustin and Witten in the geometric Langlands program arise in this way. We carry out reductions in a number of examples, and where possible present simple solutions.