We study various aspects of the 4d/3d reduction of N = 1 dualities involving U Sp(2N c ) gauge theories with 2N f fundamentals and one antisymmetric. We discuss the non-trivial role played by the monopole superpotentials in the reduction and obtain new 3d dualities for models with both symplectic and unitary gauge groups. For N f = 4 we observe interesting webs of dualities and symmetry enhancements, recovering and extending some results already appeared in the literature.

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Motivated by the BPS/CFT correspondence, we explore the similarities be- tween the classical β-deformed Hermitean matrix model and the q-deformed matrix models associated to 3d $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories on D2×qS1 and $$ {S}_b^3 $$ S b 3 by matching parameters of the theories. The novel results that we obtain are the correlators for the models, together with an additional result in the classical case consisting of the W -algebra representation of the generating function. Furthermore, we also obtain surprisingly simple expressions for the expectation values of characters which generalize previously known results.

Within the framework of four dimensional conformal supergravity we consider N = 1, 2, 3, 4 supersymmetric theories generally twisted along the abelian subgroups of the R-symmetry and possibly other global symmetry groups. Upon compactification on constant curvature Riemann surfaces with arbitrary genus we provide an extensive classification of the resulting two dimensional theories according to the amount of supersymmetry that is preserved. Exploiting the c-extremization prescription introduced in arXiv:1211.4030 we develop a general procedure to obtain the central charge for 2d N = (0, 2) theories and the expression of the corresponding R-current in terms of the original 4d one and its mixing with the other abelian global currents.