Bubbling phenomenon for Hermitian Yang-Mills connections

TL;DR

This paper constructs local examples of singular Hermitian Yang-Mills connections in three complex dimensions that have bounded energy but an arbitrarily large number of essential singular points.

Contribution

It introduces new local examples demonstrating the bubbling phenomenon in Hermitian Yang-Mills connections with bounded energy and multiple singularities.

Findings

Existence of singular Hermitian Yang-Mills connections with bounded energy

Arbitrarily large number of essential singular points in constructed examples

Insights into the bubbling phenomenon in complex gauge theory

Abstract

We construct local examples of singular Hermitian Yang-Mills connections over $B_1\subset \mathbb{C}^3$ with uniformly bounded $L^2$-energy, but the number of essential singular points can be arbitrarily large.