2020/06/24 by Gavin Ball, Gonçalo Oliveira, Goncalo Oliveira
Mathematics · Physics and Astronomy · #Curvature #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Hermitian manifold #Hermitian matrix #Hermitian symmetric space #Instanton #Invariant (physics) #Kähler manifold #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Symplectic geometry #math-ph #math.DG #math.MP #math.SG #msc:53C07 #msc:53C15 #msc:53C30
paper · pdf · doi:10.1007/s00220-021-04206-8
28 pages, 2 figures
arxiv created 2020/06/24 · openalex publication_date 2021/10/15 · arxiv updated 2021/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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-Kähler manifolds. These are constructed for all homogeneous almost Hermitian structures on the manifold of full flags in ℂ3. 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-Kähler analogue of passing a stability wall, which in string theory can be interpreted as supersymmetry breaking by internal gauge fields.