The Kähler potential of Abelian Higgs vortices

We calculate the Kähler potential for the Samols metric on the moduli space of Abelian Higgs vortices on R2, in two different ways. The first uses a scaling argument. The second depends on a variant of the relationship between accessory parameters and the regularized action in Liouville field theory. The Kähler potential on the moduli space of vortices on H2 is also derived, and we are led to a geometrical reinterpretation of these vortices.