Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(3): 737-746

Online first article May 10, 2017      Printed May 31, 2017

https://doi.org/10.4134/BKMS.b151070

Copyright © The Korean Mathematical Society.

Existence theorem for non-Abelian vortices in the Aharony--Bergman--Jafferis--Maldacena theory

Ruifeng Zhang and Meili Zhu

College of Mathematics and Statistics Henan University, Chunlai Senior High School of Chunlai Eduction Group

Abstract

In this paper, we discuss the existence theorem for multiple vortex solutions in the non-Abelian Chern--Simons--Higgs field theory developed by Aharony, Bergman, Jafferis, and Maldacena, on a doubly periodic domain. The governing equations are of the BPS type and derived by Auzzi and Kumar in the mass-deformed framework labeled by a continuous parameter. Our method is based on fixed point method.

Keywords: non-Abelian gauge field, Chern--Simons vortex equation, ABJM mode, a fixed-point method

MSC numbers: 35J20, 35J50, 35Q

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