Affine Yang-Mills-Higgs metrics

TL;DR

This paper establishes a correspondence between polystability and the existence of affine Yang-Mills-Higgs metrics for flat Higgs bundles on compact special affine manifolds with affine Gauduchon metrics.

Contribution

It proves a new equivalence between polystability and the existence of affine Yang-Mills-Higgs metrics in this geometric setting.

Findings

Polystability of flat Higgs bundles is equivalent to admitting an affine Yang-Mills-Higgs metric.

The result extends the Hitchin-Kobayashi correspondence to the affine setting.

Provides a characterization of flat Higgs bundles via differential geometric conditions.

Abstract

Let (E, \varphi) be a flat Higgs bundle on a compact special affine manifold M equipped with an affine Gauduchon metric. We prove that (E, \varphi) is polystable if and only if it admits an affine Yang-Mills-Higgs metric.