that the probe action is indeed proportional to $N$. We will not always show this dependence explicitly in what follows. Following , we find the Taylor expansion of  exactly matches the super Yang-Mills effective action   after identifying

$$a\bar{a}={1\over T_{3}\lambda}\varphi\bar{\varphi},\qquad
    (F_{s,\alpha\beta}F_{s}{}^{\alpha\beta})=
    {1\over 4T_{3}\lambda}
    (F_{f,\alpha\beta}F_{f}{}^{\alpha\beta})$$

where $F_{s,\alpha\beta}$ is the field strength appearing on the probe worldvolume and $F_{f,\alpha\beta}$ is the field strength of the field theory. Note that $\tau_{2}$ appearing in  is the classical coupling plus all instanton corrections. The fact that the four derivative terms are independent of $\tau_{2}$ shows that the supergravity result explicitly reproduces the nonrenormalization theorem for these terms.

In this section we consider the supergravity background corresponding to the case where all flavor multiplets of the field theory on the probe world volume have a mass. In this case, both the effective coupling and the four derivative terms get contributions from instantons. We are able to show that the supergravity solution is capable of producing what is expected for the one instanton correction. We are not however able to fix the coefficient of this correction. The dilaton of the supergravity solution is no longer a constant and there are corrections to the AdS$_{5}$ geometry reflecting the fact 