  We study the space of vacua of three-dimensional $\mathcal{N}=4$ theories
from a novel approach building on the type IIB brane realization of the theory
and in which the insertion of local chiral operators in the path integral is
obtained from integrating out light modes in appropriate brane setups. Most of
our analysis focuses on abelian quiver theories which can be realized as the
low-energy theory of D3-D5-NS5 brane arrays. Their space of vacua contains a
Higgs branch, parametrized by the vevs of half-BPS meson operators, and a
Coulomb branch, parametrized by the vevs of half-BPS monopole operators. We
show that the Higgs operators are inserted by adding F1 strings and D3 branes,
while the Coulomb operators are inserted by adding D1 strings and D3 branes,
with specific orientations, to the initial brane setup of the theory. This
approach has two main advantages. First the ring relations describing the Higgs
and Coulomb branches can be derived by looking at specific brane setups with
multiple interpretations in terms of operator insertions. This provides a new
derivation of the Coulomb branch quantum relations. Secondly the map between
the Higgs and Coulomb operators of mirror dual theories is obtained in a
trivial way from IIB S-duality.
