The Role of Conformal Symmetry in the Jackiw-Pi Model

TL;DR

This paper investigates how conformal symmetry behaves in the quantum version of the Jackiw-Pi model, showing that it is preserved at specific coupling values where vortex solutions exist, due to a vanishing beta-function.

Contribution

It provides the first-order quantum corrections to the Jackiw-Pi model and demonstrates conditions under which conformal symmetry remains intact at the quantum level.

Findings

Beta-function vanishes at g^2 = +/- e^2

Conformal symmetry is preserved when vortex solutions exist

Only the coupling constant g^2 requires renormalization

Abstract

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^2 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 beta-function. However, the beta-function vanishes upon restricting the coupling constants to values g^2 = +/- e^2, which includes the case in which vortex solutions exist. Therefore the existence of vortices also guarantees the preservation of the conformal symmetries.