2006/01/31 by Masashi Hamanaka · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1016/j.nuclphysb.2006.02.014
published as Nucl.Phys.B741:368-389,2006 · 29 pages, LaTeX; v2: reduction to NC Tzitzeica modified, minor changes
openalex publication_date 2006/02/22 · arxiv created 2006/03/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Noncommutative Ward's conjecture is a noncommutative version of the original Ward's conjecture which says that almost all integrable equations can be obtained from anti-self-dual Yang-Mills equations by reduction. In this paper, we prove that wide class of noncommutative integrable equations in both (2+1)- and (1+1)-dimensions are actually reductions of noncommutative anti-self-dual Yang-Mills equations with finite gauge groups, which include noncommutative versions of Calogero-Bogoyavlenskii-Schiff eq., Zakharov system, Ward's chiral and topological chiral models, (modified) Korteweg-de Vries, Non-Linear Schroedinger, Boussinesq, N-wave, (affine) Toda, sine-Gordon, Liouville, Tzitzeica, (Ward's) harmonic map eqs., and so on. This would guarantee existence of twistor description of them and the corresponding physical situations in N=2 string theory, and lead to fruitful applications to noncommutative integrable systems and string theories. Some integrable aspects of them are also discussed.