Analytic Approach for Computation of Topological Number of Integrable Vortex on Torus
arXiv:2403.18264 · doi:10.1007/JHEP09(2024)189
Abstract
An analytic method to calculate the vortex number on a torus is constructed, focusing on analytic vortex solutions to the Chern-Simons-Higgs theory, whose governing equation is the so-called Jackiw-Pi equation. The equation is one of the integrable vortex equations and is reduced to Liouville's equation. The requirement of continuity of the Higgs field strongly restricts the characteristics and the fundamental domain of the vortices. Also considered are the decompactification limits of the vortices on a torus, in which "flux loss" phenomena occasionally occur.
25 pages, 9 figures
References in corpus (8)
- Water-Wave Vortices and Skyrmions
- Instanton constituents in the O(3) model at finite temperature
- Integrability of Vortex Equations on Riemann Surfaces
- Non-Abelian Vortices on Riemann Surfaces: an Integrable Case
- Five Vortex Equations
- Magnetic Impurities, Integrable Vortices and the Toda Equation
- Mock-integrability and stable solitary vortices
- Cartan Connections and Integrable Vortex Equations