  We analyze exactly marginal deformations of 3d 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 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.
