Year: 2026
Type: preprint
Abstract: We classify entire stable solutions with quadratic energy growth in the $4$-dimensional abelian Higgs model. More precisely, we prove that such solutions are holomorphic with respect to some complex structure, namely they satisfy the first order equations introduced by Bradlow, and consequently their nodal sets are holomorphic curves. Conversely, we construct solutions whose nodal set is any prescribed holomorphic curve with quadratic area growth. As a corollary, we show that all stable solutions with linear energy growth in $\mathbb{R}^3$ are two-dimensional Bogomolnyi vortices.
Source: arXiv (Cornell University)
Author: Badran, Marco
Institutions: ETH Zurich, Bocconi University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212294660