Andrei Domrin
Noncommutative unitons
A solution of the noncommutative $U(n)$ sigma-model is said to be
finite-type if it may be presented as a finite-dimensional
perturbation of a solution of energy~0. We show that every
finite-type solution admits a factorization into unitons, which
is a noncommutative analogue of Uhlenbeck's description of harmonic
maps from $S^2$ to $U(n)$. As a corollary, we establish the phenomenon
of quantization of energy for such solutions and obtain an explicit
description of the moduli space of finite-type solutions for small
values of energy. We also use the uniton factorization to construct
large families of previously unknown ``genuinely non-Grassmannian''
solutions.
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