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arXiv · hep-th/9204056

Chern-Simons Solitons, Toda Theories and the Chiral Model

Gerald Dunne·Roman Jackiw
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Abstract

The two-dimensional self-dual Chern--Simons equations are equivalent to the conditions for static, zero-energy solutions of the $(2+1)$-dimensional gauged nonlinear Schrödinger equation with Chern--Simons matter-gauge dynamics. In this paper we classify all finite charge $SU(N)$ solutions by first transforming the self-dual Chern--Simons equations into the two-dimensional chiral model (or harmonic map) equations, and then using the Uhlenbeck--Wood classification of harmonic maps into the unitary groups. This construction also leads to a new relationship between the $SU(N)$ Toda and $SU(N)$ chiral model solutions.

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Gerald Dunne, Roman Jackiw. 1992-04-17. Chern-Simons Solitons, Toda Theories and the Chiral Model. https://doi.org/10.1007/bf02096959

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