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arXiv · 1212.3561

Vortices as degenerate metrics

J. M. Baptista
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Abstract

We note that the Bogomolny equation for abelian vortices is precisely the condition for invariance of the Hermitian-Einstein equation under a degenerate conformal transformation. This leads to a natural interpretation of vortices as degenerate hermitian metrics that satisfy a certain curvature equation. Using this viewpoint, we rephrase standard results about vortices and make new observations. We note the existence of a conceptually simple, non-linear rule for superposing vortex solutions, and we describe the natural behaviour of the L^2-metric on the moduli space upon restriction to a class of submanifolds.

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J. M. Baptista. 2013-04-04. Vortices as degenerate metrics. https://doi.org/10.1007/s11005-014-0683-4

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