Noncommutative solitons.(English)Zbl 1183.83069

Macías, Alfredo (ed.) et al., Recent developments in gravitation and cosmology. 3rd Mexican meeting on mathematical and experimental physics, México City, México, 10–14 September 2007. Proceedings. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0496-0/hbk). AIP Conference Proceedings 977, 37-51 (2008).
Summary: 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.
For the entire collection see [Zbl 1175.83004].

MSC:

 83C65 Methods of noncommutative geometry in general relativity 35Q51 Soliton equations
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