Exploring Seiberg-like Dualities with Eight Supercharges

We propose a family of IR dualities for 3d $\mathcal{N}=4$ $U(N)$ SQCD with $N_f$ fundamental flavors and $P$ Abelian hypermultiplets i.e. $P$ hypermultiplets in the determinant representation of the gauge group. These theories are good in the Gaiotto-Witten sense if the number of fundamental flavors obeys the constraint $N_f \geq 2N-1$ with generic $P \geq 1$, and in contrast to the standard $U(N)$ SQCD, they do not admit an ugly regime. The IR dualities in question arise in the window $N_f=2N+1,2N,2N-1,$ with $P=1$ in the first case and generic $P \geq 1$ for the others. The dualities involving $N_f=2N \pm 1$ are characterized by an IR enhancement of the Coulomb branch global symmetry on one side of the duality, such that the rank of the emergent global symmetry group is greater than the rank of the UV global symmetry. The dual description makes the rank of this emergent global symmetry manifest in the UV. In addition, one can read off the emergent global symmetry itself from the dual quiver. We show that these dualities are related by certain field theory operations and assemble themselves into a duality web. Finally, we show that the $U(N)$ SQCDs with $N_f \geq 2N-1$ and $P$ Abelian hypers have Lagrangian 3d mirrors, and this allows one to explicitly write down the 3d mirror associated with a given IR dual pair. This paper is the first in a series of four papers on 3d $\mathcal{N}=4$ Seiberg-like dualities.