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.
Soojung Kim, Youngae Lee
Soongsil University; Kyungpook National University
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).
2007; 44(3): 511-523
2010; 47(4): 831-843
2012; 49(1): 153-164
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd