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Uniqueness of topological solutions for the Gudnason model

이영애|김수정
대한수학회 (The Korean Mathematical Society)|2021.07|대한수학회지 (Journal of the KMS)|제58권 제4호|pp. 873-894|DOI 10.4134/JKMS.j200294

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키워드

perturbationUniquenesstopological solutionGreen representation formuladoubly periodic solution
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초록

In this paper, we consider the Gudnason model of $\mathcal{N} = 2$ supersymmetric field theory, where the gauge field dynamics is governed by two Chern-Simons terms. Recently, it was shown by Han et al. that for a prescribed configuration of vortex points, there exist at least two distinct solutions for the Gudnason model in a flat two-torus, where a sufficient condition was obtained for the existence. Furthermore, one of these solutions has the asymptotic behavior of topological type. In this paper, we prove that such doubly periodic topological solutions are uniquely determined by the location of their vortex points in a weak-coupling regime.

Abstract

In this paper, we consider the Gudnason model of $\mathcal{N} = 2$ supersymmetric field theory, where the gauge field dynamics is governed by two Chern-Simons terms. Recently, it was shown by Han et al. that for a prescribed configuration of vortex points, there exist at least two distinct solutions for the Gudnason model in a flat two-torus, where a sufficient condition was obtained for the existence. Furthermore, one of these solutions has the asymptotic behavior of topological type. In this paper, we prove that such doubly periodic topological solutions are uniquely determined by the location of their vortex points in a weak-coupling regime.

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