BOGOMOL'NYI VORTICES FROM SEIBERG–WITTEN MONOPOLES

International Journal of Modern Physics A (IJMPA)

Year: 1999 Vol: 14 Issue: 24 (30 September 1999) Page: 3905 - 3920

SAZZAD MAHMUD NASIR
Department of Theoretical Physics, Box 803, S-75 108 Uppsala, Sweden.
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, England

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.