The role of conformal symmetry in the Jackiw-Pi model

The Jackiw-Pi model in 2+1 dimensions is a non-relativistic conformal field theory of charged particles with point-like self-interaction. For specific values of the interaction strengths the classical theory possesses vortex and multi-vortex solutions, which are all degenerate in energy. We compute the full set of first-order perturbative quantum corrections. Only the coupling constant g2 requires renormalization; the fields and electric charge e are not renormalized. It is shown that in general the conformal symmetries are broken by an anomalous contribution to the conservation law, proportional to the β-function. However, the β-function vanishes upon restricting the coupling constants to values g2=±e2, which includes the case in which vortex solutions exist. Therefore the existence of vortices also guarantees the preservation of the conformal symmetries.