Interplay of generalised symmetries and moduli spaces in 3d N=5 SCFTs

The moduli space and generalised global symmetries of 3d N=5 superconformal field theories are investigated, with a focus on the orthosymplectic ABJ theories and their discrete gauging variants. We extend the known classification of N=5 moduli spaces as orbifolds H2N/Γ, where Γ is a quaternionic reflection group, to theories incorporating Spin, O-, and Pin-type gauge groups. In these cases, we find that the moduli space is governed not by Γ itself, but by a Z2 central extension thereof, for which we explicitly describe the generators. We provide a systematic method to construct the group Γ′ governing the moduli space of a theory T′ obtained by gauging a Z2 zero-form symmetry of an original theory T. This is achieved by identifying the specific generator that must be added to Γ. We compute the Hilbert series for these moduli spaces and verify them against the corresponding limits of the superconformal index, finding perfect agreement. We also discuss how ’t Hooft anomalies for the zero-form symmetries manifest in the superconformal index and the moduli space. Furthermore, we revisit the symmetry category of the so(2N)2k x usp(2N)-k theories. Building on previous work that identified the symmetry category for all parities of N and k, we provide the explicit symmetry webs for the opposite parity D8 case. We find that the details of these webs differ from the previously studied D8 webs corresponding to the both even parity case. Finally, we analyse theories with unequal ranks, those containing the so(2N + 1) gauge algebra, and the two SCFT variants based on the F(4) superalgebra.