N=4 Super Yang-Mills Theory on the Coulomb Branch
It is conjectured that the world-volume action of a probe D3-brane in an AdS_5XS^5 background of type IIB superstring theory, with one unit of flux, can be
reinterpreted as the exact effective action for U(2) N =4 super Yang-Mills theory
on the Coulomb branch. An analogous conjecture for ABJM theory
is also presented. The main evidence supporting these conjectures is that
the brane actions have all of the expected symmetries and dualities.