Vortices as degenerate metrics

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.

15 pages; v2: expanded introduction and additional observations in the last section

References in corpus (1)

• On the L^2-metric of vortex moduli spaces

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