to constant gauge fields on the brane have zero momentum along the brane .

In this section we study the static quark-antiquark potential, in the large $|\varphi|$ region where the background geometry described above is valid. This corresponds to studing the effects of instantons on the static quark-antiquark potential in the large $N$ field theory. There is a large body of evidence from lattice calculations that indicate that instanton effects play a major role in the physics of light hadrons. Below we will argue that the supergravity description provides a powerful new approach to these questions.

The energy of a quark-antiquark pair can be read off of the expectation value of a Wilson loop. This Wilson loop is identified with a fundamental string ending on the boundary of the asymptotically AdS$_{5}$ space. The Wilson loop configuration is thus obtained by minimizing the Nambu-Goto action

$$S={1\over 2\pi}\int d\tau d\sigma\int\sqrt{det(g_{MN}
\partial_{\alpha}x^{M}\partial_{\beta}x^{N})}$$

The metric $g_{MN}$ felt by the strings is not the Einstein metric , but rather the string frame metric. We are interested in a static string configuration and take $\sigma=x^{1}$ and $\tau=x^{0}$. The string is at a fixed $x^{2},x^{3},x^{4},x^{5},x^{6},x^{7}$ and $\theta$ where $\theta$ is the angular variable in the $(8,9)$ plane. 