Communications in Mathematical Physics

, Volume 150, Issue 3, pp 519–535 | Cite as

Chern-Simons solitons, Toda theories and the chiral model

  • Gerald Dunne


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 chargeSU(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 theSU(N) Toda andSU(N) chiral model solutions.


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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Gerald Dunne
    • 1
  1. 1.Department of Mathematics and Center for Theoretical PhysicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Physics DepartmentUniversity of ConnecticutStorrsUSA

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