Uniqueness Of The Topological Multivortex Solution In The Self-dual Chern-simons Theory

JOURNAL OF MATHEMATICAL PHYSICS 46, 012305 (2005) Uniqueness of the topological multivortex solution in the self-dual Chern–Simons theory Kwangseok Choea) Department of Mathematics, Seoul National University, Seoul 151-747, Korea (Received 7 July 2004; accepted 24 September 2004; published online 5 January 2005) We establish a uniqueness result for the topological multivortex solution to the self-dual equations of the Abelian relativistic self-dual Chern–Simons–Higgs model. We prove that the topological multivortex solution is unique if the Chern– Simons coupling parameter ␬ ⬎ 0 is sufficiently small. We also establish a uniqueness result for ␬ ⬎ 0 sufficiently large. © 2005 American Institute of Physics. [DOI: 10.1063/1.1834694] I. INTRODUCTION Chern–Simons theories have attracted much attention as they are believed relevant to physical phenomena such as high-temperature superconductivity and anyon physics. In particular, Hong–Kim–Pac18 and Jackiw–Weinberg19 proposed an Abelian Chern–Simons–Higgs model whose dynamics is governed only by the Chern–Simons term. This model is given in the (2⫹1)dimensional Minkowski space with metric g␮␯ = diag共1 , −1 , −1兲. When a suitable Higgs potential is chosen, this model admits a self-dual structure which enables us to study the static solutions rigorously. The Lagrangian density18,19 is given by 1 ␬ L = ␧␮␯␳F␮␯A␳ + g␮␯D␮␾D␯␾ − 2 兩␾兩2共1 − 兩␾兩2兲2 , 4 ␬ where A␮ 共␮ = 0 , 1 , 2兲 is a real gauge field on R3, ␾ is the complex-valued Higgs fiel