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The Jackiw-Pi model in 2+1 dimensions is a non-relativistic conformal fieldtheory of charged particles with point-like self-interaction. For specificvalues of the interaction strengths the classical theory possesses vortex andmulti-vortex solutions, which are all degenerate in energy. We compute the fullset of first-order perturbative quantum corrections. Only the coupling constantg^2 requires renormalization; the fields and electric charge e are notrenormalized. It is shown that in general the conformal symmetries are brokenby an anomalous contribution to the conservation law, proportional to thebeta-function. However, the beta-function vanishes upon restricting thecoupling constants to values g^2 = +/- e^2, which includes the case in whichvortex solutions exist. Therefore the existence of vortices also guarantees thepreservation of the conformal symmetries.

The Role of Conformal Symmetry in the Jackiw-Pi Model