Seiberg-like dualities for 3d \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N}=2 $\end{document} theories with SU(N) gauge group

We work out Seiberg-like dualities for 3d \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N}=2 $\end{document} theories with SU(N) gauge group. We use the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathrm{SL}\left( {2,\mathbb{Z}} \right) $\end{document} action on 3d conformal field theories with U(1) global symmetry. One of generator S of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathrm{SL}\left( {2,\mathbb{Z}} \right) $\end{document} acts as gauging of the U(1) global symmetry. Utilizing S = S−1 up to charge conjugation, we obtain Seiberg-like dual of an SU(N) theory by gauging topological U(1) symmetry of the Seiberg-like dual of the U(N) theory with the same matter content. We work out the Aharony dualities for SU(N) gauge theory with Nf fundamental flavors, with/without one adjoint matter with the superpotential. We also work out the Giveon-Kutasov duality for the SU(N) gauge theory with Chern-Simons term and with Nf fundamental flavors. For all the proposed dualities, we give various evidences such as chiral ring matching and the superconformal index computation. We find the perfect matching.