  We compare two applications of the gauge/gravity correspondence to a non
conformal gauge theory, based respectively on the study of D-branes wrapped on
supersymmetric cycles and of fractional D-branes on orbifolds. We study two
brane systems whose geometry is dual to N=4, D=2+1 super Yang-Mills theory, the
first one describing D4-branes wrapped on a two-sphere inside a Calabi-Yau
two-fold and the second one corresponding to a system of fractional
D2/D6-branes on the orbifold R^4/Z_2. By probing both geometries we recover the
exact perturbative running coupling constant and metric on the moduli space of
the gauge theory. We also find a general expression for the running coupling
constant of the gauge theory in terms of the "stringy volume" of the two-cycle
which is involved in both types of brane systems.
