Monopole operators and symmetry enhancement in ABJM theory revisited

Abstract

We construct monopole operators for 3D Yang-Mills matter theories and Chern-Simons matter theories in canonical formalism. In this framework, monopole operators, although they are disorder operators, could be written in terms of the fundamental fields of the theory, and thus could be treated in the same way as the ordinary operators. We study the properties of the constructed monopole operators. In Chern-Simons matter theories, monopole operators transform as the local operators with the classical conformal dimension 0 under the action of the dilation and are also covariantly constant. In supersymmetric Chern-Simons matter theories like the ABJM model, monopole operators commute with all of the supercharges, and thus are SUSY invariant. The ABJM model with level $k=1,2$ is expected to have enhanced $SO(8)$ R symmetry due to the existence of the conserved extra R-symmetry currents ${j}_{\ensuremath{\mu}}^{AB}$ involving monopoles. With the explicit form of the monopole operators given, we prove the current conservation equation ${\ensuremath{\partial}}^{\ensuremath{\mu}}{j}_{\ensuremath{\mu}}^{AB}=0$ using the equations of motion. We also compute the extra $\mathcal{N}=2$ supercharges, derive the extra $\mathcal{N}=2$ SUSY transformation rules, and verify the closure of the $\mathcal{N}=8$ supersymmetry.