Mixed moduli in 3d $$ \mathcal{N} $$ = 4 higher-genus quivers

We analyze exactly marginal deformations of 3d $$ \mathcal{N} $$ N = 4 Lagrangian gauge theories, especially mixed-branch operators with both electric and magnetic charges. These mixed-branch moduli can either belong to products of electric and magnetic current supermultiplets, or be single-trace (non-factorizable). Apart from some exceptional quivers that have additional moduli, 3d $$ \mathcal{N} $$ N = 4 theories described by genus g quivers with nonabelian unitary gauge groups have exactly g single-trace mixed moduli, which preserve the global flavour symmetries. This partly explains why only linear and circular quivers have known AdS 4 supergravity duals. Indeed, for g > 1, AdS 4 gauged supergravities cannot capture the entire g -dimensional moduli space even if one takes into account the quantization moduli of boundary conditions. Likewise, in a general Lagrangian theory, we establish (using the superconformal index) that the number of single-trace mixed moduli is bounded below by the genus of a graph encoding how nonabelian gauge groups act on hypermultiplets.