TL;DR
This paper explores the construction, properties, and dynamics of noncommutative solitons in various gauge theories, revealing new solutions and connections to integrable systems, supersymmetry, and string theory.
Contribution
It introduces the moduli spaces and dynamics of Moyal-deformed solitons in 2+1D Yang-Mills-Higgs theory and relates them to integrable models and twistor string theory.
Findings
Constructed noncommutative solitons in gauge theories.
Connected noncommutative solitons to integrable systems like sine-Gordon.
Extended the framework to supersymmetric models.
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.
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