On the gauge/gravity correspondence and the open/closed string duality.

We compute the annulus diagram corresponding to the interaction of a fractional D3 brane with a gauge field on its world-volume and a stack of N fractional D3 branes on the orbifolds C2 /Z2 and C3 /(Z2 × Z2 ). We show that its logarithmic divergence can be equivalently understood as due either to massless open string states circulating in the loop or to massless closed string states exchanged between two boundary states. This follows from the fact that, under open/closed string duality, massless states in the open and closed string channels are matched into each other without mixing with massive states. This explains why the perturbative properties of many gauge theories living on the world- volume of less supersymmetric and nonconformal branes have been recently obtained from their corresponding supergravity solution.