Mixed Chern-Simons theories admit Bogomol'nyi equations for dyonic vortex-antivortex systems with Bradlow bounds that limit total vortex number in vortex-only cases but only the net difference in mixed cases.
Bogomol’nyi, The stability of classical solutions,Sov
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Bogomol'nyi Equations in Mixed Product Chern-Simons Theories Governing Charged Vortices and Antivortices
Mixed Chern-Simons theories admit Bogomol'nyi equations for dyonic vortex-antivortex systems with Bradlow bounds that limit total vortex number in vortex-only cases but only the net difference in mixed cases.