2006/04/30 by Michael Klawunn, Olaf Lechtenfeld, Stefan Petersen · 14 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Equations of motion #Grassmannian #Integrable system #Mathematical physics #Mathematics #Moduli space #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Physics #Pure mathematics #Quantum mechanics #Sigma #Sigma model #Soliton #hep-th
paper · pdf · doi:10.1088/1126-6708/2006/06/028
published in Journal of High Energy Physics 2006(06), 028 (Springer Nature) · 1+15 pages, 2 figures; v2: reference added, to appear in JHEP
arxiv created 2006/06/07 · openalex publication_date 2006/06/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model solitons to generic scalar-field solitons for an infinitely stiff potential. The static k-lump moduli space Ck/Sk features a natural K"ahler metric induced from an embedding Grassmannian. The moduli-space dynamics is blind against adding a WZW-like term to the sigma-model action and thus also applies to the integrable U(1) Ward model. For the latter's two-soliton motion we compare the exact field configurations with their supposed moduli-space approximations. Surprisingly, the two do not match, which questions the adiabatic method for noncommutative solitons.