KNOTTED SELF-DUAL VORTEX IN GENERALIZED ABELIAN CHERN–SIMONS HIGGS FIELD

Abstract

Based on the Bogomol'nyi self-dual equation in the Abelian Chern–Simons Higgs model, we find a self-dual topological term which was ignored all the time in the Bogomol'nyi self-duality equation due to the improper decomposition of the complex Higgs field. We also present a generalized self-dual equation for the first time which unified the topological term and nontopological term in (2+1) space–time. It is shown that the self-dual vortex just arise from the symmetric phase of the Higgs field ϕ = 0, this provides a deep insight into the spontaneous symmetry breaking mechanism. When generalizing this model into (3+1) space–time, we show that the topological number on a family of knotted vortex are just the sum of linking number and self-linking number. We also find this topological charge is conserved during the splitting, the mergence and the intersection processes of knotted vortex lines.