理论物理中心学术报告

Date: 2017.06.02 (Friday) 2PM
Place: Rm 220, Physics Building, Sichuan University
Speaker: Prof. Sven Bjarke Gudnason (Institute of Modern Physics, CAS)
[visit from 06.01 - 06.06]

Title: Some exact Bradlow vortex solutions

Abstract:
I will discuss Manton's five vortex equations, the action giving rise the generic equation and a different toy model giving rise to the Bradlow equation. The integrable cases have a geometric interpretation and are related to the vortex map (squared) being a ratio of the Baptista metric to the background metric. Both metrics give rise to constant Gaussian curvatures, except at the vortex positions where the Baptista metric has conical singularities with a conical excess of 2\pi per vortex. The Gaussian curvature of the background metric is given by the (Fayet-Iliopoulos) constant in the vortex equation and the Gaussian curvature of the Baptista metric is given by the constant multiplying the scalar field (squared). All the known integrable cases have constant background curvature. For the Bradlow vortex, it is not necessary, though, due to the simplicity of the equation. I present some simple solutions with non-constant Gaussian background curvature. The Bradlow equation has the peculiarity that on a noncompact manifold, it gives rise to either infinitely many topological vortices or a finite number of nontopological vortices. Finally, I will contemplate possible physical interpretations related to BEC systems with constant magnetic fields. [Based on 1701.04356]