Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the circle reduction of twisted A2N theories of class S in four dimensions. Although these quivers bear a resemblance to the star-shaped quivers previously studied in the literature, they contain unitary, symplectic and special orthogonal gauge groups, along with hypermultiplets in the fundamental representation. The vacuum moduli spaces of these quiver theories are studied in detail. The Coulomb branch Hilbert series of the mirror theory can be matched with that of the Higgs branch of the corresponding four dimensional theory, providing a non-trivial check of our proposal. Moreover various deformations by mass and Fayet-Iliopoulos terms of such quiver theories are investigated. The fact that several of them flow to expected theories also gives another strong support for the proposal. Utilising the mirror quiver description, we discover a new supersymmetry enhancement renormalisation group flow.

The zero-form and one-form global symmetries of the Aharony-Bergman-Jafferis (ABJ) and related theories, with at least $$ \mathcal{N} $$ N = 6 supersymmetry in three dimensions, are examined in detail. Starting from well-known dualities between theories with orthogonal and symplectic gauge groups and those with unitary gauge groups, we gauge their one-form symmetries or their subgroups and obtain new dualities. One side of the latter involves theories with special orthogonal and symplectic gauge groups, and the other side involves theories with unitary gauge groups; there is a discrete quotient on one or both sides of the duality. We study the refined superconformal indices of such theories and map the symmetries across the dualities, with particular attention to their discrete part. As a generalisation, we also find a new duality between a circular quiver with a discrete quotient of alternating special orthogonal and symplectic gauge groups and a three-dimensional $$ \mathcal{N} $$ N = 4 circular (Kronheimer-Nakajima) quiver with unitary gauge groups, whose Higgs or Coulomb branch describes an instanton on a singular orbifold.

The study of exactly marginal deformations of superconformal field theories is a topic that has received considerable attention due to their rich properties. We investigate the $$ \mathcal{N} $$ N = 2 preserving exactly marginal operators of 3d S-fold SCFTs. Two families of such theories are considered: one is constructed by gauging the diagonal flavour symmetry of the T(U(2)) and T(U(3)) theories, and the other by gauging the diagonal flavour symmetry of the $$ {T}_{\left[2,{1}^2\right]}^{\left[2,{1}^2\right]}\left( SU(4)\right) $$ T 2 1 2 2 1 2 SU 4 theory. In both families, it is possible to turn on a Chern-Simons level for each gauge group and to couple to each theory various numbers of hypermultiplets. The detailed analysis of the exactly marginal operators, along with the superconformal indices, allows us to determine whether supersymmetry gets enhanced in the infrared and to deduce the amount of supersymmetry of the corresponding SCFT.