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.
arXiv comment1+39 pages; v2: typos corrected, refs added, final JHEP version
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- On Reductions of Noncommutative Anti-Self-Dual Yang-Mills Equations
- Spherically symmetric monopoles in noncommutative space
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- Noncommutative Instantons and Solitons
- A new approach to deformation equations of noncommutative KP hierarchies
- Noncommutative Instantons in 4k Dimensions
- Magnetic Monopole in Noncommutative Space-Time and Wu-Yang Singularity-Free Gauge Transformations
- A monopole solution from noncommutative multi-instantons
- Monopoles, noncommutative gauge theories in the BPS limit and some simple gauge groups
- Noncommutative Nonlinear Sigma Models and Integrability
- Magnetic Monopoles in Noncommutative Space-Time: Second Order of Perturbation