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Noncommutative unitons

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Abstract

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 8π, 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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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. V. Domrin

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  1. A. V. Domrin
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Correspondence to A. V. Domrin.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 220–239, February, 2008.

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Domrin, A.V. Noncommutative unitons. Theor Math Phys 154, 184–200 (2008). https://doi.org/10.1007/s11232-008-0018-7

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  • DOI: https://doi.org/10.1007/s11232-008-0018-7

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