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.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics
- Astronomy and Astrophysics