Some approaches to three-point correlators in N = 4 super Yang-Mills

AdS/CFT correspondence is the first precise realization of the gauge/string duality. Up to now AdS/CFT correspondence still remains a conjecture. The duality of N = 4 SYM and the appropriate string counterpart, type IIB string theory on the AdS₅ x S⁵ manifold, is the most notable example of the AdS/CFT correspondence. One of the main obstructions to exploring it is the fact that weak coupling regime for the gauge theory is the strong coupling regime for the string theory and vice versa. Therefore as long as perturbative methods are applied, one cannot compare the observables of dual counterparts directly apart from some specific cases. At this point the huge symmetry of N = 4 SYM plays an important role allowing exact computation of the theory observables at least in the planar limit. This thesis is devoted to computation of three-point functions, one of the main observables of N = 4 SYM, and consists of two parts. In the first part we consider the general approach for computing three-point functions based on the so-called spin vertex, which is inspired from the string field theory. In the second part we consider a specific kind of three-point functions called heavy-heavy-light, which are characterized by the property that the length of one of the operators is much smaller the lengths of other two. It happens that this kind of correlators can be considered as diagonal form factors which supposes that in this case one can apply the results obtained in the form factor theory. (author)