the sevenbranes by themselves.

Next following , we introduce threebranes into the problem. The presence of the threebranes modifies the metric and switches on a non-zero flux for the self dual RR five-form field strength. The world volume coordinates of the threebranes are $x^{0},x^{1},x^{2},x^{3}$. One obtains a valid solution by making the following ansatz for the metric

and the following ansatz for the self-dual 5-form field strength

The complex field $\tau$ is unchanged by the introduction of the threebranes. Inserting the above ansatz into the IIB supergravity equations of motion, one finds that $f$ satisfies the following equation of motion

This last equation corresponds to the case in which all of the three branes are located at the same point. In the limit that $N\to\infty$ the curvature becomes small almost everywhere and the supergravity solution can be used to reliably compute quantities in the field theory limit as explained in.

In the case of $N_f=4$ massless hypermultiplets,  is explicitly given by

The solution is given by

$$f={4N\pi\over\big[y^{2}+\tau_{2}|a|^{2}\big]^{2}}.$$

To reproduce the low energy effective action of the field theory, we now consider the dynamics of a threebrane probe moving in this geometry. It is well known that the probe has a 