  Brane Box Models of intersecting NS and D5 branes are mapped to D3 branes at
C^3/Gamma orbifold singularities and vise versa, in a setup which gives rise to
N=1 supersymmetric gauge theories in four dimensions. The Brane Box Models are
constructed on a two-torus. The map is interpreted as T-duality along the two
directions of the torus. Some Brane Box Models contain NS fivebranes winding
around (p,q) cycles in the torus, and our method provides the geometric T-dual
to such objects. An amusing aspect of the mapping is that T-dual configurations
are calculated using D=4 N=1 field theory data. The mapping to the singularity
picture allows the geometrical interpretation of all the marginal couplings in
finite field theories. This identification is further confirmed using the
AdS/CFT correspondence for orbifold theories. The AdS massless fields coupling
to the marginal operators in the boundary appear as stringy twisted sectors of
S^5/Gamma. The mapping for theories which are non-finite requires the
introduction of fractional D3 branes in the singularity picture.
