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Chern-Simons vortices

In (2+1) dimensions, the Maxwell term $-(1/4) F_{αβ}F^{αβ}$ can be replaced by the Chern-Simons three-form $(κ/4)ε^{αβγ}A_αF_{βγ}$, yielding a novel type of `electromagnetism'. This has been proposed for studying the Quantum Hall Effect as well as High-Temperature Superconductivity. The gauge field can be coupled to a scalar field either relativistically or non-relativistically. In both cases, one admits finite-energy, vortex solutions.