  We study the boundary vertex algebras of $A$-twisted $\mathcal{N}=4$ Abelian
gauge theories in three dimensions. These are identified with the BRST quotient
(semi-infinite cohomology) of collections of symplectic bosons and free
fermions that reflect the matter content of the corresponding gauge theory. We
develop various free field realisations for these vertex algebras which we
propose to interpret in terms of their localisation on their associated
varieties. We derive the free field realisations by bosonising the elementary
symplectic bosons and free fermions and then calculating the relevant
semi-infinite cohomology, which can be done systematically. An interesting
feature of our construction is that for certain preferred free field
realisations, the outer automorphism symmetry of the vertex algebras in
question (which are identified with the symmetries of the Coulomb branch in the
infrared) are made manifest.
