Vortices as degenerate metrics
| Autor: | Baptista, J. M. |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Lett. Math. Phys. 104: 731-747, 2014 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11005-014-0683-4 |
| Popis: | 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. Comment: 15 pages; v2: expanded introduction and additional observations in the last section |
| Databáze: | arXiv |
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