Noncommutative Solitons
arXiv:0710.2074 · doi:10.1063/1.2902796
Abstract
Solitonic objects play a central role in gauge and string theory (as, e.g., monopoles, black holes, D-branes, etc.). Certain string backgrounds produce a noncommutative deformation of the low-energy effective field theory, which allows for new types of solitonic solutions. I present the construction, moduli spaces and dynamics of Moyal-deformed solitons, exemplified in the 2+1 dimensional Yang-Mills-Higgs theory and its Bogomolny system, which is gauge-fixed to an integrable chiral sigma model (the Ward model). Noncommutative solitons for various 1+1 dimensional integrable systems (such as sine-Gordon) easily follow by dimensional and algebraic reduction. Supersymmetric extensions exist as well and are related to twistor string theory.
16 pages; talk given at the Third Mexican Meeting on Mathematical and Experimental Physics at El Colegio Nacional, Mexico City, 10-14 September 2007
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- Bäcklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations
- Soliton Scattering in Noncommutative Spaces
- Quantum aspects of a noncommutative supersymmetric kink
- Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates
- Structure of Noncommutative Solitons: Existence and Spectral Theory
- Dispersion Estimates for the Discrete Laguerre Operator
- Noncommutative Baby Skyrmions
- Dynamics of Noncommutative Solitons II: Spectral Theory, Dispersive Estimates and Stability
- Exact BPS bound for noncommutative baby Skyrmions