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Vortices as Degenerate Metrics

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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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  1. Centre for Mathematical Analysis, Geometry, and Dynamical Systems (CAMGSD), Instituto Superior Técnico, University of Lisbon, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    Joao M. Baptista

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  1. Joao M. Baptista
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Correspondence to Joao M. Baptista.

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Baptista, J.M. Vortices as Degenerate Metrics. Lett Math Phys 104, 731–747 (2014). https://doi.org/10.1007/s11005-014-0683-4

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  • DOI: https://doi.org/10.1007/s11005-014-0683-4

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