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We study a three-dimensional $\mathcal{N}=2$ supersymmetric $G_2$ gaugetheory with and without fundamental matters. We find that a classical Coulombbranch of the moduli space of vacua is partly lifted by monopole-instantons andthe quantum Coulomb moduli space would be described by a complexone-dimensional space. Depending on the number of the matters in a fundamentalrepresentation, the low-energy dynamics of the theory shows various phases likes-confinement or quantum merging of the Coulomb and the Higgs branches. We alsoinvestigate superconformal indices as an independent check of our analysis.

Low-Energy Dynamics of 3d $\mathcal{N}=2$ $G_2$ Supersymmetric Gauge Theory