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New Faddeev-Niemi-Type variables for the static Yang-Mills theory

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Abstract

Faddeev and Niemi introduced a nonlinear sigma model as a natural extension of the Faddeev \(\mathbb{S}^2 \) chiral model. The field variables in the extended model are two chiral fields taking values in SU(3)/(U(1)×U(1)) and SU(3)/(SU(2)×U(1)). Shabanov showed that the energy functional of the extended model is bounded from below by a topological invariant and can therefore support knotlike excitations and a mass gap. We introduce new variables of the Faddeev-Niemi type for the static SU(3) Yang-Mills theory, which reveal a structure of a nonlinear sigma model in the Lagrangian.

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Authors and Affiliations

  1. Institute of Theoretical Physics, University of Warsaw, Warsaw, Poland

    M. Kisielowski

  2. St. Petersburg Department of Steklov Institute of Mathematics, RAS, St. Petersburg, Russia

    M. Kisielowski

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  1. M. Kisielowski
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Correspondence to M. Kisielowski.

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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 176, No. 2, pp. 222–253, August 2013.

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Kisielowski, M. New Faddeev-Niemi-Type variables for the static Yang-Mills theory. Theor Math Phys 176, 1016–1043 (2013). https://doi.org/10.1007/s11232-013-0088-z

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