The dynamics of vortices on S2 near the Bradlow limit

The explicit solutions of the Bogomolny equations for N vortices on a sphere of radius R-2>N are not known. In particular, this has prevented the use of the geodesic approximation to describe the low energy vortex dynamics. In this article we introduce an approximate general solution of the equations, valid for R(2)greater than or similar toN, which has many properties of the true solutions, including the same moduli space CPN. Within the framework of the geodesic approximation, the metric on the moduli space is then computed to be proportional to the Fubini-Study metric, which leads to a complete description of the particle dynamics. (C) 2003 American Institute of Physics.