Bogomol'nyi Equations and Coexistence of Vortices and Antivortices in Generalized Abelian Higgs Theories
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909833533325312 |
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| 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 |
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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 |