• 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. 

## 1.4 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. 

## 1.4.1 Premise 

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 

