Integrable Chern-Simons Gauge Field Theory in 2+1 Dimensions

Details Integrable Chern-Simons Gauge Field Theory in 2+1 Dimensions Integrable Chern-Simons Gauge Field Theory in 2+1 Dimensions

1995-05-30

arxiv.org/abs/hep-th/9505178v1

Mod.Phys.Lett. A11 (1996) 1713-1728

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, plain Tex

Scientific paper

The classical spin model in planar condensed media is represented as the U(1) Chern-Simons gauge field theory. When the vorticity of the continuous flow of the media coincides with the statistical magnetic field, which is necessary for the model's integrability, the theory admits zero curvature connection. This allows me to formulate the model in terms of gauge - invariant fields whose evolution is described by the Davey-Stewartson (DS) equations. The Self-dual Chern-Simons solitons described by the Liouville equation are subjected to corresponding integrable dynamics. As a by-product the 2+1-dimensional zero-curvature representation for the DS equation is obtained as well as the new reduction conditions related to the DS-I case. Some possible applications for the statistical transmutation in the anyon superfluid and TQFT are briefly discussed.

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