|DATE||September 20 (Thu), 2018|
|INSTITUTE||University of Leeds|
|TITLE||The geometry of the space of vortex-antivortex pairs|
In the linear abelian Higgs model on a Riemann surface, vortices and antivortices attract one another and annihilate. By contrast, gauged nonlinear sigma models have vortices and antivortices which can coexist in stable equilibrium, at arbitrary positions. The moduli space of static k_+ vortex k_- antivortex solutions is noncompact even in the case when physical space is compact, since vortices and antivortices are forbidden to coincide, and is equipped with a natural Kaehler structure whose geodesics model low energy (anti)vortex scattering trajectories. I will describe a detailed study (joint with Nuno Romao) of this Kaehler geometry, concentrating on the case of vortex-antivortex pairs (k_+=k_-=1) on the plane and the sphere.