Andrei Domrin
Noncommutative unitons
A solution of the noncommutative $U(n)$ sigmamodel is said to be
finitetype if it may be presented as a finitedimensional
perturbation of a solution of energy~0. We show that every
finitetype 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 finitetype solutions for small
values of energy. We also use the uniton factorization to construct
large families of previously unknown ``genuinely nonGrassmannian''
solutions.
