The DT-instanton equation on almost Hermitian 6-manifolds

TL;DR

This paper explores the DT-instanton equations on almost Hermitian 6-manifolds, providing the first examples of non-Abelian solutions on non-Kähler manifolds and analyzing their stability and classification.

Contribution

It introduces the first non-Abelian, irreducible DT-instantons on non-Kähler manifolds and classifies homogeneous solutions for all structures on the flag manifold in $\,\mathbb{C}^3$.

Findings

Constructed explicit non-Abelian DT-instantons on non-Kähler manifolds.

Classified homogeneous DT-instantons for all structures on the flag manifold.

Observed phenomena of irreducible instantons becoming reducible and disappearing as structures vary.

Abstract

This article investigates a set of partial differential equations, the DT-instanton equations, whose solutions can be regarded as a generalization of the notion of Hermitian-Yang-Mills connections. These equations owe their name to the hope that they may be useful in extending the DT-invariant to the case of symplectic 6-manifolds. In this article, we give the first examples of non-Abelian and irreducible DT-instantons on non-K\"ahler manifolds. These are constructed for all homogeneous almost Hermitian structures on the manifold of full flags in $\mathbb{C}^3$. Together with the existence result we derive a very explicit classification of homogeneous DT-instantons for such structures. Using this classification we are able to observe phenomena where, by varying the underlying almost Hermitian structure, an irreducible DT-instanton becomes reducible and then disappears. This is a non-K\"ahler analogue of passing a stability wall, which in string theory can be interpreted as supersymmetry breaking by internal gauge fields.