Chern-Simons Solitons, Toda Theories and the Chiral Model

Details Chern-Simons Solitons, Toda Theories and the Chiral Model Chern-Simons Solitons, Toda Theories and the Chiral Model

1992-04-17

arxiv.org/abs/hep-th/9204056v1

Commun.Math.Phys. 150 (1992) 519-535

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1007/BF02096959

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 Schr\"odinger 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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