2004/07/02 by Heng-Yu Chen, N. S. Manton · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Geometry and complex manifolds #hep-th
paper · pdf · doi:10.1063/1.1874334
published as J.Math.Phys. 46 (2005) 052305 · 25 pages
arxiv created 2004/07/02 · arxiv updated 2009/12/01
We calculate the Kähler potential for the Samols metric on the moduli space of Abelian Higgs vortices on \mathbbmR2, 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 \mathbbmH2 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 \mathbbmR2 in a third way by relating the vortices to SU(2) Yang-Mills instantons on \mathbbmR2× S2. This approach does not give the correct result, and we offer a possible explanation for this.