The extended Bogomolny equations on $\mathbb {R}^2 \times \mathbb {R}^+$ I: Nilpotent Higgs field

Panagiotis Dimakis

The extended Bogomolny equations on $\mathbb {R}^2 \times \mathbb {R}^+$ I: Nilpotent Higgs field

Mathematical Physics 2024-01-31 v2 Analysis of PDEs Differential Geometry math.MP

Authors: Panagiotis Dimakis

Abstract

We study the extended Bogomolny equations with gauge group $SU(2)$ on $\mathbb {R}^2 \times \mathbb {R}^+$ with generalized Nahm pole boundary conditions and nilpotent Higgs field. We completely classify solutions by relating them to certain holomorphic data through a Kobayashi-Hitchin correspondence.

Keywords

extended bogomolny equations gauge group su(2) nahm pole nilpotent higgs field kobayashi-hitchin correspondence holomorphic data

Cite

@article{arxiv.2209.11101,
  title  = {The extended Bogomolny equations on $\mathbb {R}^2 \times \mathbb {R}^+$ I: Nilpotent Higgs field},
  author = {Panagiotis Dimakis},
  journal= {arXiv preprint arXiv:2209.11101},
  year   = {2024}
}