Noncommutative Monopoles and Riemann-Hilbert Problems

Details Noncommutative Monopoles and Riemann-Hilbert Problems Noncommutative Monopoles and Riemann-Hilbert Problems

2003-06-26

arxiv.org/abs/hep-th/0306263v2

JHEP 0401 (2004) 069

Physics

High Energy Physics

High Energy Physics - Theory

1+39 pages; v2: typos corrected, refs added, final JHEP version

Scientific paper

10.1088/1126-6708/2004/01/069

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.

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