Bogomol'nyi Equations and Coexistence of Vortices and Antivortices in Generalized Abelian Higgs Theories

Fuente: arXiv
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Main Authors: Xu, Aonan, Yang, Yisong
Format: Preprint
Published: 2025
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_version_ 1866909833533325312
author Xu, Aonan
Yang, Yisong
author_facet Xu, Aonan
Yang, Yisong
contents We derive the Bogomol'nyi equations in generalized Abelian Higgs theories which allow the coexistence of vortices and antivortices over a compact Riemann surface or the full plane. In the compact surface situation, we obtain a necessary and sufficient condition for the existence of a unique solution describing a system of coexisting vortices and antivortices. In the full-plane situation, we prove the existence of a unique solution representing an arbitrary distribution of vortices and antivortices and obtain sharp asymptotic behavior of the solution near infinity. These solutions carry quantized magnetic fluxes and energies explicitly expressed in terms of the numbers of vortices and antivortices topologically characterized by the first Chern and Thom classes.
format Preprint
id arxiv_https___arxiv_org_abs_2505_02162
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Bogomol'nyi Equations and Coexistence of Vortices and Antivortices in Generalized Abelian Higgs Theories
Xu, Aonan
Yang, Yisong
Mathematical Physics
High Energy Physics - Phenomenology
High Energy Physics - Theory
35J50, 53C43, 81T13
We derive the Bogomol'nyi equations in generalized Abelian Higgs theories which allow the coexistence of vortices and antivortices over a compact Riemann surface or the full plane. In the compact surface situation, we obtain a necessary and sufficient condition for the existence of a unique solution describing a system of coexisting vortices and antivortices. In the full-plane situation, we prove the existence of a unique solution representing an arbitrary distribution of vortices and antivortices and obtain sharp asymptotic behavior of the solution near infinity. These solutions carry quantized magnetic fluxes and energies explicitly expressed in terms of the numbers of vortices and antivortices topologically characterized by the first Chern and Thom classes.
title Bogomol'nyi Equations and Coexistence of Vortices and Antivortices in Generalized Abelian Higgs Theories
topic Mathematical Physics
High Energy Physics - Phenomenology
High Energy Physics - Theory
35J50, 53C43, 81T13
url https://arxiv.org/abs/2505.02162