Abstract
The Seiberg-Witten monopole equations are studied on manifolds of type X = Σ × S2, where Σ is a Riemann surface of genus g > 1. Imposing spherical symmetry on the monopole equations, Bogomol'nyi vortices on Σ are obtained. The dimensions of the two moduli spaces agree. As a consistency check, we show that all solutions to the monopole equations on X that descend to Σ are spherically symmetric. Further, Bogomol'nyi vortices on S2 are obtained as dimensional reduction of the monopole equations on S2. Finally, the Seiberg-Witten "invariant" in these cases are briefly discussed.
Original language | English (US) |
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Pages (from-to) | 3905-3920 |
Number of pages | 16 |
Journal | International Journal of Modern Physics A |
Volume | 14 |
Issue number | 24 |
DOIs | |
State | Published - Sep 30 1999 |
Funding
I am very much indebted to Professor N. S. Manton for suggesting this problem to me and for discussions that I have had with him during the course of this work. I would also like to thank Dr. C. Houghton and Dr. H. Merabet for helpful comments on this manuscript. This work was supported by the Overseas Research Scheme, the Cambridge Commonwealth Trust and Wolfson college.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics
- Astronomy and Astrophysics