Abstract
Using a noncommutative version of the uniton theory, we study the space of those solutions of the noncommutative U(1) sigma model that are representable as finite-dimensional perturbations of the identity operator. The basic integer-valued characteristics of such solutions are their normalized energy e, canonical rank r, and minimum uniton number u, which always satisfy r ≤ e and u ≤ e. Starting with the so-called BPS solutions (u = 1), we completely describe the sets of all solutions with r = 1, 2, e − 1, e (which forces u ≤ 2) and all solutions of small energy (e ≤ 5). The obtained results reveal a simple but nontrivial structure of the moduli spaces and lead to a series of conjectures.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 307–327, September, 2008.
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Domrin, A.V. Moduli spaces of solutions of a noncommutative sigma model. Theor Math Phys 156, 1231–1246 (2008). https://doi.org/10.1007/s11232-008-0103-y
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DOI: https://doi.org/10.1007/s11232-008-0103-y