Fermionic quantization of Hopf solitons

In this paper we show how to quantize Hopf solitons using the Finkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions if their Hopf charge is odd. Symmetries of classical minimal energy configurations induce loops in configuration space which give rise to constraints on the wave function. These constraints depend on whether the given loop is contractible. Our method is to exploit the relationship between the configuration spaces of the Faddeev-Hopf and Skyrme models provided by the Hopf fibration. We then use recent results in the Skyrme model to determine whether loops are contractible. We discuss possible quantum ground states up to Hopf charge Q=7

Exact moduli space metrics for hyperbolic vortex polygons

Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted as Sigma_{n,m}, are spaces of C_n-invariant vortex configurations with n single vortices at the vertices of a regular polygon and m=N?n coincident vortices at the polygon's center. The geometric properties of Sigma_{n,m} are investigated, and it is found that Sigma_{n,n?1} is isometric to the hyperbolic plane of curvature ?(3 pi n)^{?1}. The geodesic flow on Sigma_{n,m} and a geometrically natural variant of geodesic flow recently proposed by Collie and Tong [“The dynamics of Chern-Simons vortices,” Phys. Rev. D Part. Fields Gravit. Cosmol. 78, 065013 (2008);e-print arXiv:hep-th/0805.0602] are analyzed in detail