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arXiv · hep-th/0407011

The Kähler Potential of Abelian Higgs Vortices

Heng-Yu Chen·N. S. Manton
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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.

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Heng-Yu Chen, N. S. Manton. 2004-07-02. The Kähler Potential of Abelian Higgs Vortices. https://doi.org/10.1063/1.1874334

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