• 1/N expansion Once again, mirroring the techniques of perturbation theory, experi- mental quantities are calculated as a perturbative expansion in terms of the N in the SU ( N ) of the gauge group of QCD, in line with the argument presented in section 1.2.5. In theory this is applicable to all of QCD, but the perturbation parameter, (1 / 3) $^{2}$, is not very small, so the series does not converge as quickly as one might like. More importantly, it is not clear how to go about calculating the 1/N cor- rections. Hence there is little knowledge of the error in a tree-level calculation. The AdS-CFT correspondence falls under this classifica- tion. Before we investigate it we need to go over some basic aspects of string theory. The AdS/CFT correspondence is discussed in detail in chapter 2. It de- scribes a duality between a gauge theory and a string theory, so we take this opportunity to review some of those aspects of string theory relevant to this thesis. String theory starts by assuming that fundamental particles are not point- like, but have a finite length. In other words, they are little strings. We reach the Euler-Lagrange equations of motion for point-like particles by minimizing their world-lines. By analogy, we assume that the equations of motion for strings will be found by minimizing their world areas. The original formula for the area of the sheet, known as the Nambu-Goto action 26 1.4 String Theory 1.4.1 Premise