The Kähler Potential of Abelian Higgs Vortices

Abstract

We calculate the Kähler potential for the Samols metric on the moduli space of Abelian Higgs vortices on $\mathbbm{R}^{2}$, 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 $\mathbbm{H}^{2}$ 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 $\mathbbm{R}^{2}$ in a third way by relating the vortices to SU(2) Yang-Mills instantons on $\mathbbm{R}^{2}\times S^{2}$. This approach does not give the correct result, and we offer a possible explanation for this.

25 pages

Cited by in corpus (16)

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• Vortex Motion on Surfaces of Small Curvature
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• Vortices on Hyperbolic Surfaces
• Dynamics of Non-Abelian Vortices
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• Small Winding-Number Expansion: Vortex Solutions at Critical Coupling
• Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface
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