I've been studying IR-dualities in 2+1 dimensions. I encountered monopole operators in the following paper:

Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)d

On page 10, starting from $QED_{3}$ with $N_{f}$ fermions of charge 1, the monopole operator is defined in the following way. Let $\left\{a_{i},a_{j}^{\dagger}\right\}=\delta_{ij}$ be the annihilation and creation operators for the zero-modes of the Dirac fermion in the monopole background. Let $\left|0\right>$ be the bare monopole state. Then the monopole operator is defined to be associated with the state. $$\left|\mathfrak{M}_{i_{1} i_{2}\cdots i_{l}}\right>=a_{i_{1}}a_{i_{2}}\cdots a_{i_{l}}\left|0\right>$$ This state transforms in totally anti-symmetric representation of $SU(N_{f})$, with $l$ indices, and is bosonic.

Could anyone please help me understand this definition? Why is monopole operator defined in such a way? How do I see that it transforms in representation of $SU(N_{f})$? Why is it bosonic?


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