# Coulomb Branch vs. Higgs Branch (and the connection with D-branes, AdS/CFT)

I am confused about the difference between the Coulomb and Higgs branches of the moduli space of supersymmetric gauge theories. It's easy to find a definition for $D=4$, $\mathcal{N}=2$ supersymmetric field theories: The moduli space is locally a direct product between the two branches: $\mathcal{M} = \mathcal{M}_C \times \mathcal{M}_H$. The Coulomb branch corresponds to scalar fields in the vector multiplet getting VEV's, and the Higgs branch corresponds to scalar fields in the hypermultiplet getting VEV's.

I'm interested in this question for the case of $D=4$, $\mathcal{N}=4$ SYM, i.e. the worldvolume theory of D3-branes. Again, it's easy to find statements to the effect that the Coulomb branch corresponds to separating the D3 branes in the transverse directions, which gives mass to the some of the gauge fields and thus Higgses them. My main question is: what is the brane interpretation of the Coulomb branch?