Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons

TL;DR

This paper establishes a link between Spin(7)-instantons on an 8D manifold and non-Abelian vortex equations on 2D space, revealing novel non-holomorphic Higgs field features in supersymmetric gauge theories.

Contribution

It introduces a new class of non-Abelian vortex equations derived from Spin(7)-instantons, highlighting non-holomorphic Higgs fields in supersymmetric gauge theories.

Findings

G-invariant Spin(7)-instantons correspond to non-Abelian vortices on R^2.

Higgs fields in these vortices are generally non-holomorphic.

BPS vortex equations in N=4 super Yang-Mills share similar features.

Abstract

We consider a complex vector bundle E endowed with a connection A over the eight-dimensional manifold R^2 x G/H, where G/H = SU(3)/U(1)xU(1) is a homogeneous space provided with a never integrable almost complex structure and a family of SU(3)-structures. We establish an equivalence between G-invariant solutions A of the Spin(7)-instanton equations on R^2 x G/H and general solutions of non-Abelian coupled vortex equations on R^2. These vortices are BPS solitons in a d=4 gauge theory obtained from N=1 supersymmetric Yang-Mills theory in ten dimensions compactified on the coset space G/H with an SU(3)-structure. The novelty of the obtained vortex equations lies in the fact that Higgs fields, defining morphisms of vector bundles over R^2, are not holomorphic in the generic case. Finally, we introduce BPS vortex equations in N=4 super Yang-Mills theory and show that they have the same feature.