On the existence of harmonic metrics on non-Hermitian Yang-Mills bundles

TL;DR

This paper proves that harmonic metrics exist on non-Hermitian Yang-Mills bundles over compact Kähler manifolds if and only if these bundles are semisimple, confirming a key conjecture in the field.

Contribution

It establishes the equivalence between the existence of harmonic metrics and semisimplicity for NHYM bundles, confirming a significant conjecture.

Findings

Harmonic metrics exist iff NHYM bundles are semisimple

Confirms Conjecture 8.7 in 

Advances understanding of non-Hermitian Yang-Mills theory

Abstract

In this paper, we study the non-Hermitian Yang-Mills (NHYM for short) bundles over compact K\"ahler manifolds. We show that the existence of harmonic metrics is equivalent to the semisimplicity of NHYM bundles, which confirms the Conjecture 8.7 in \cite{KV}.