Mathematics – Mathematical Physics
Scientific paper
Feb 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008tmp...154..184d&link_type=abstract
Theoretical and Mathematical Physics, Volume 154, Issue 2, pp.184-200
Mathematics
Mathematical Physics
1
Noncommutative Sigma Model, Uniton Factorization
Scientific paper
By Uhlenbeck’s results, every harmonic map from the Riemann sphere S2 to the unitary group U(n) decomposes into a product of so-called unitons: special maps from S2 to the Grassmannians Gr k(ℂn) ⊂ 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 π, 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.
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