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Nonlinear sigma models solvable by the Aratyn-Ferreira-Zimerman ansatz

Minoru Hirayama·Chang-Guang Shi
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Abstract

Nonlinear sigma models compatible with the aratyn-Ferreira-Zimerman ansatz are discussed, the latter ansatz automatically leading to configurations with definite values of the Hopf index. These models are allowed to involve a weight factor which is a function of one of the toroidal coordinates. Depending on the choice of the weight factor, the field equation takes various forms. In one model with a special weight factor, the field equation turns out to be the fifth Painleve equation. This model suggests the existence of a knot soliton strictly confined in a finite spatial volume. Some other interesting cases are also discussed.

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Minoru Hirayama, Chang-Guang Shi. 2002-02-15. Nonlinear sigma models solvable by the Aratyn-Ferreira-Zimerman ansatz. https://doi.org/10.1103/physrevd.65.065008

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