Noncommutative unitons

By Uhlenbeck's results, every harmonic map from the Riemann sphere $S^2$ to the unitary group $U(n)$ decomposes into a product of so-called unitons: special maps from $S^2$ to the Grassmannians $\mathrm{Gr}_k(\mathbb C^n)\subset U(n)$ satisfying certain systems of first-order differential equations. We construct a noncommutative analogue of this factorization, applicable to those solutions of the noncommutative unitary sigma model that are finite-dimensional perturbations of zero-energy solutions. In particular, we prove that the energy of each such solution is an integer multiple of $8\pi$, give examples of solutions that are not equivalent to Grassmannian solutions, and study the realization of non-Grassmannian zero modes of the Hessian of the energy functional by directions tangent to the moduli space of solutions.