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Non-abelian vortices on CP^1 and Grassmannians
Many properties of the moduli space of abelian vortices on a compact Riemann surface are known. For non-abelian vortices the moduli space is less well understood. Here we consider non-abelian vortices on the Riemann sphere CP^1, and we study their moduli spaces near the Bradlow limit. We give an exp...
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Published in: | arXiv.org 2013-04 |
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Main Author: | |
Format: | Article |
Language: | English |
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Online Access: | Get full text |
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Summary: | Many properties of the moduli space of abelian vortices on a compact Riemann surface are known. For non-abelian vortices the moduli space is less well understood. Here we consider non-abelian vortices on the Riemann sphere CP^1, and we study their moduli spaces near the Bradlow limit. We give an explicit description of the moduli space as a Kahler quotient of a finite-dimensional linear space. The dimensions of some of these moduli spaces are derived. Strikingly, there exist non-abelian vortex configurations on CP^1, with non-trivial vortex number, for which the moduli space is a point. This is in stark contrast to the moduli space of abelian vortices. For a special class of non-abelian vortices the moduli space is a Grassmannian, and the metric near the Bradlow limit is a natural generalization of the Fubini--Study metric on complex projective space. We use this metric to investigate the statistical mechanics of non-abelian vortices. The partition function is found to be analogous to the one for abelian vortices. |
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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.1211.1662 |