Noncommutative unitons
Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 2, pp. 220-239
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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.
Keywords:
noncommutative sigma model, uniton factorization.
@article{TMF_2008_154_2_a1,
author = {A. V. Domrin},
title = {Noncommutative unitons},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {220--239},
publisher = {mathdoc},
volume = {154},
number = {2},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a1/}
}
A. V. Domrin. Noncommutative unitons. Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 2, pp. 220-239. http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a1/