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 is related to the Polyakov conjecture 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. Finally, we attempt to find the Kähler potential for vortices on R2 in a third way by relating the vortices to SU(2) Yang-Mills instantons on R2 × S2. This approach does not give the correct result, and we offer a possible explanation for this. email [email protected] email [email protected]