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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.08822 |
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| _version_ | 1866910204941041664 |
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| author | Xu, Aonan |
| author_facet | Xu, Aonan |
| contents | We extend product Chern-Simons theory to develop several mixed $U(1)\times U(1)$ models where one gauge field is governed by a Chern-Simons term and the other by a Maxwell or Born-Infeld term. We show that, by choosing suitable potentials, the energy functional admits a topological lower bound saturated by first-order self-dual equations. The resulting dyonic systems can be divided into vortex-vortex and vortex-antivortex configurations, and the coexistence of vortices and antivortices in the latter extends the vortex-only result known in product Chern-Simons model. On a doubly periodic domain, we establish Bradlow-type bounds with distinct physical implications: for vortex-only systems, the vortex numbers stay below this bound and cannot be arbitrarily large; for vortex-antivortex systems, the bound is imposed on the difference between the vortex and antivortex numbers, while the individual numbers are arbitrary. This distinction results in a bounded energy spectrum for the former and an unbounded energy spectrum for the latter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08822 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bogomol'nyi Equations in Mixed Product Chern-Simons Theories Governing Charged Vortices and Antivortices Xu, Aonan High Energy Physics - Theory High Energy Physics - Phenomenology Mathematical Physics 35J50, 53C43, 58E15, 81T13, 82B26 We extend product Chern-Simons theory to develop several mixed $U(1)\times U(1)$ models where one gauge field is governed by a Chern-Simons term and the other by a Maxwell or Born-Infeld term. We show that, by choosing suitable potentials, the energy functional admits a topological lower bound saturated by first-order self-dual equations. The resulting dyonic systems can be divided into vortex-vortex and vortex-antivortex configurations, and the coexistence of vortices and antivortices in the latter extends the vortex-only result known in product Chern-Simons model. On a doubly periodic domain, we establish Bradlow-type bounds with distinct physical implications: for vortex-only systems, the vortex numbers stay below this bound and cannot be arbitrarily large; for vortex-antivortex systems, the bound is imposed on the difference between the vortex and antivortex numbers, while the individual numbers are arbitrary. This distinction results in a bounded energy spectrum for the former and an unbounded energy spectrum for the latter. |
| title | Bogomol'nyi Equations in Mixed Product Chern-Simons Theories Governing Charged Vortices and Antivortices |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology Mathematical Physics 35J50, 53C43, 58E15, 81T13, 82B26 |
| url | https://arxiv.org/abs/2605.08822 |