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Coulomb branch in 3d $\mathcal{N}=2$ $SU(N)_k$ Chern-Simons gauge theories with chiral matter content

We elaborate on quantum moduli spaces in 3d $\mathcal{N}=2$ $SU(N)_k$ Chern-Simons gauge theories with $F$ fundamental and $\bar{F}$ anti-fundamental matter fields. The quantum flat direction on the Coulomb branch differs so much from the classical one and from the one of the vector-like theories. In many cases, the Coulomb branch is parametrized by the dressed monopoles. As is found from the computation of the superconformal index, these dressed operators at first sight appear to be dressed by massive elementary fields which don't seem to contribute to the low-energy physics. We argue that these dressed fields can be interpreted as a non-abelian monopole dressed (or not dressed) by massless matter fields. Based on this analysis, we will report on the s-confinement phases with non-trivial monopole operators, which is consistent with the duality proposals \cite{Aharony:2014uya, Aharony:2013dha}. Along these studies, we find that the duality reported in \cite{Aharony:2014uya} must be modified when $k=\pm \frac{1}{2}(F-\bar{F})$ in order to have a correct duality map of the baryonic operators.