a}-{b\over a^{2}})}}
\int_{r_{0}}^{\infty}dy\left(
{\sqrt{(y^{4}-{b\over a})}
\over\sqrt{y^{4}+r_{0}^{4}}}-1\right).$$

To extract the dependence of this energy on the quark-antiquark separation $L$ we need to determine $r_{0}$ as a function of $L$. The expression for the energy given above is identical to the static potential for the quark-antiquark pair in the ${\cal N}=4$ theory at finite temperature. &gt;From the results of  we know that $E(L)$ has the form

$$E=-{c_{1}\over L}-c_{2}L^{3}.$$

The constant $c_{1}$ is positive. In the limit that $m_{i}\to 0$, $c_{2}\to 0$ and we regain the ${1\over L}$ dependence, a fact which is determined by conformal invariance. The sign of the constant $c_{2}$ is dependent on $\theta.$ For $c_{2}$ positive (negative) we have a screening (antiscreening) of the quark-antiquark pair due to the instantons. This expression can’t be trusted for very large $L$: for larger and larger $L$ the Wilson loop is able to move further and further into the bulk. Our solution is however only valid for large $r$, so that the Wilson loop begins to explore regions in the bulk for which our solution is not valid. The long distance behaviour of the quark-antiquark potential could be extracted from the exact supergravity background.

In this section we obtain the leading correction 