Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2021; 58(4): 873-894

Online first article December 2, 2020      Printed July 1, 2021

https://doi.org/10.4134/JKMS.j200294

Copyright © The Korean Mathematical Society.

Uniqueness of topological solutions for the Gudnason model

Soojung Kim, Youngae Lee

Soongsil University; Kyungpook National University

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.

Keywords: Uniqueness, topological solution, Green representation formula, perturbation, doubly periodic solution

MSC numbers: 35J47, 35A02, 35J08, 35B20, 35B06

Supported by: S. Kim was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. NRF-2018R1C1B6003051). Y. Lee was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. NRF-2018R1C1B6003403).