Note on Monopole Operators in Chern-Simons-Matter Theories

Monopole operators in Chern-Simons theories with charged matter have been studied using the state-operator map in CFTs, as states on ℝ × S$^{2}$ with background magnetic flux on S$^{2}$. Gauge invariance requires a dressing with matter modes which provides non-zero spin to the monopoles. In this note we propose a description of the monopole operators directly on ℝ$^{3}$, as a singular behavior of the gauge and matter fields in the vicinity of the insertion point, with a dressing. We study abelian theories with a charged boson or a charged fermion. We extend the discussion to abelian supersymmetric Chern-Simons-matter theories and describe the BPS monopoles, which have spin and preserve a single supercharge. We match our results against the prediction from the superconformal index.