ar X iv : h ep - t h / 94 10 06 5 v 1 1 0 O ct 1 99 4 Self - Dual Chern - Simons Theories ∗
نویسنده
چکیده
In these lectures I review classical aspects of the self-dual Chern-Simons systems which describe charged scalar fields in 2 + 1 dimensions coupled to a gauge field whose dynamics is provided by a pure Chern-Simons Lagrangian. These self-dual models have one realization with nonrelativistic dynamics for the scalar fields, and another with relativistic dynamics for the scalars. In each model, the energy density may be minimized by a Bogomol’nyi bound which is saturated by solutions to a set of first-order self-duality equations. In the nonrelativistic case the self-dual potential is quartic, the system possesses a dynamical conformal symmetry, and the self-dual solutions are equivalent to the static zero energy solutions of the equations of motion. The nonrelativistic self-duality equations are integrable and all finite charge solutions may be found. In the relativistic case the self-dual potential is sixth order and the self-dual Lagrangian may be embedded in a model with an extended supersymmetry. The self-dual potential has a rich structure of degenerate classical minima, and the vacuum masses generated by the Chern-Simons Higgs mechanism reflect the self-dual nature of the potential.
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ar X iv : h ep - t h / 95 03 06 1 v 1 9 M ar 1 99 5 Spinor vortices in non - relativistic Chern - Simons theory
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