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arXiv 2602.17857hep-thmath-phmath.MP
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Chern-Simons变形的带约束O(3)西格玛模型在紧致曲面上的解

Chern-Simons deformations of the gauged O(3) Sigma model on compact surfaces

Instituto de Matemáticas, Universidad Nacional Autónoma de México（墨西哥国立自治大学数学研究所）

Rene I. Garcia-Lara

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34 pages, 2 figures
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AI总结：

研究了带约束O(3)西格玛模型在紧致曲面上的Chern-Simons变形解的存在性及多解性，探讨了旋涡与反旋涡数目的影响及Maxwell极限。

摘要：

在紧致黎曼面上，通过拓扑方法证明了带约束Chern-Simons-O(3)西格玛模型场方程的解的存在性。证明了存在一个最小的变形常数κ* > 0，使得对于任意给定的旋涡和反旋涡配置，当|κ| ≤ κ*时至少存在一个解。对于较小的Chern-Simons变形参数κ，当旋涡和反旋涡总数不同时，场方程允许多个解。计算了场方程解的Maxwell极限。相反，当旋涡数等于反旋涡数时，证明对于任何κ值，场方程至少存在一个解，并且证明了κ→∞的极限。在球面上对变形参数的依赖性进行了数值研究。

英文摘要：

Existence of solutions to the field equations of the gauged Chern-Simons-O(3)-Sigma model on a compact Riemann surface is proved by a topological method. Existence of a minimal deformation constant $κ_{*} > 0$ is proved, such that for any prescribed configuration of vortices and antivortices, at least one solution exists for $|κ| \leq κ_{*}$. For small values of the Chern-Simons deformation parameter $κ$, it is proved that the field equations admit multiple solutions, provided the total number of vortices and antivortices are different. The Maxwell limit is computed for solutions of the field equations. In contrast, if the number of vortices equals the number of antivortices, it is proved that the field equations admit at least one solution for any value of $κ$ and the limit $κ\to \infty$ is proved. dependence of the fields on the deformation parameter is investigated numerically on the sphere.

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