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 g 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 g = ±e, which includes the case in which vortex solutions exist. Therefore the existence of vortices also guarantees the preservation of the conformal symmetries.