Abstract
Recently an algorithm to dualize a theory into its mirror dual has been proposed, both for 3d mathcal{N} = 4 linear quivers and for their 4d mathcal{N} = 1 uplift. This mimics the manipulations done at the level of the Type IIB brane setup that engineers the 3d theories, where mirror symmetry is realized as S-duality, but it is enirely field-theoretic and based on the application of genuine infra-red dualities that implement the local action of S-duality on the quiver. In this paper, we generalize the algorithm to the full duality group, which is SL(2, ℤ) in 3d and PSL(2, ℤ) in 4d. This also produces dualities for 3d mathcal{N} = 3 theories with Chern-Simons couplings, some of which have enhanced mathcal{N} = 4 supersymmetry, and their new 4d mathcal{N} = 1 counterpart. In addition, we propose three ways to study the RG flows triggered by possible VEVs appearing at the last step of the algorithm, one of which uses a new duality that implements the Hanany-Witten move in field theory.
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