Noncommutative Monopoles and Riemann-Hilbert Problems
arXiv:hep-th/0306263 · doi:10.1088/1126-6708/2004/01/069
Abstract
The Bogomolny equations for Yang-Mills-Higgs monopoles follow from a system of linear equations which may be solved through a parametric Riemann-Hilbert problem. We extend this approach to noncommutative R^3 and use it to (re)construct noncommutative Dirac, Wu-Yang, and BPS monopole configurations in a unified manner. In all cases we write down the underlying matrix-valued functions for multi-monopoles and solve the corresponding Riemann-Hilbert problems for charge one.
1+39 pages; v2: typos corrected, refs added, final JHEP version