  We study the vacuum moduli spaces of 3d N=2 supersymmetric quantum field
theories by applying the formalism developed in our previous paper
arXiv:1404.5527. The 3d theories can be realized by branes in type IIB string
theory, which in a decoupling limit reduce to 4d N=4 super-Yang-Mills theory on
an interval with BPS defects inserted. The moduli space of a given 3d theory is
obtained by solving a generalization of Nahm's equations with appropriate
boundary/junction conditions, along with help from the S-duality of type IIB
string theory. Our classical computations reproduce many known results about
the quantum-corrected moduli spaces of 3d theories, e.g. U(N_c) theories with
N_f flavors with mass and FI parameters turned on. In particular, our methods
give first-principles derivations of several results in the literature,
including the s-rule, quantum splitting of classical Coulomb branches, the
lifting of the Coulomb branch by non-Abelian instantons, quantum merging of
Coulomb and Higgs branches, and phase transitions from re-ordering 5-branes.
