On marginal deformations of N = 4 super Yang–Mills theory

In this Thesis I analyze some aspects of a class of quantum field theories that can be obtained by marginally deforming N=4 SYM theory. These theories constitue a very non trivial example of N=1 superconformal actions in four dimensional space-time and play a role in the context of AdS/CFT. I begin by introducing superfield notations and constructing deformed theories following Leigh and Strassler procedure. Then an analysis of the finiteness properties of the actions is performed. Considering different specific cases, solutions of the superconformal constraint are given. The issues of conformal invariance and finiteness in the case of complex and real beta-deformed models are addressed. In the real beta case an all loop solution of the constraint is provided. In the case of complex deformation, it turns out that the condition of vanishing beta function leads to a result which is scheme dependent. In the second part of the work, anomalous dimensions of composite operators are computed. A new method for extracting protected operators in the chiral sector is introduced. Using the proposed procedure it is possible to gain a loop order in perturbative computations with respect to canonical methods. The structure of the chiral ring of the deformed theories is then classified up to three loops.