Orthosymplectic quivers: indices, Hilbert series, and generalised symmetries

A bstract We investigate generalised global symmetries in 3d N=4 N = 4 orthosymplectic quiver gauge theories. Using the superconformal index, we identify a D 8 categorical symmetry web in a class of theories featuring so (2N) usp (2N) so 2 N × usp 2 N gauge algebra (at zero Chern-Simons levels) and n bifundamental half-hypermultiplets, analogous to ABJ-type models. As a distinct contribution, we improve the prescription, previously studied in the literature, for computing Coulomb branch Hilbert series of SO (N) gauge theories with N f vector hypermultiplets. Our improved prescription extends these methods by incorporating fugacities for discrete zero-form symmetries — specifically charge conjugation and magnetic symmetries — and properly treating background magnetic fluxes for the flavour symmetry. This refinement enables calculations for various global forms (O (N) ±, Spin (N), Pin (N) ) and ensures consistency with the Coulomb branch limit of the superconformal index and known dualities. The proper treatment of fluxes is particularly essential for analysing orthosymplectic quivers where such a flavour symmetry is gauged. We verify our methods through several examples, including an analysis of the mapping of discrete symmetries under mirror symmetry for T SO (N) and T USp (2 N) theories. The analysis also readily generalises to the T ρ SO (N) and T ρ USp (2 N) theories associated with partition ρ.