SCATTERING AMPLITUDES IN SUPERCONFORMAL GAUGE THEORIES

Superconformal field theories have been widely explored over the last years, especially because of their large amount of symmetry which allows to derive exact results. The most prominent example within this class is the four-dimensional maximally supersymmetric N = 4 Super Yang-Mills theory, which played a pivotal role in the proposal of the AdS/CFT correspondence, a conjectured weak/strong duality relating superconformal gauge theories to string theories on curved backgrounds. Soon after the formulation of the correspondence the presence of integrable structures was discovered both in planar N = 4 SYM and in its string counterpart, and since then integrability in superconformal theories became one of the main research topics in theoretical physics. Interestingly, integrability in N = 4 was later shown to be intimately related to the presence of the so called dual conformal symmetry, a hidden symmetry of the planar amplitudes that puts even stronger constraints on their structure. This suggests that some crucial aspects of a theory can be investigated through the computation of its scattering amplitudes, which can thereby provide a powerful tool also for the study of less supersymmetric superconformal field theories. In particular it is essential to understand whether some of the beautiful properties of N = 4 survives when supersymmetry is not maximal. In this thesis we present computations of massless scattering amplitudes in two different not maximally supersymmetric conformal theories: N = 2 superconformal QCD in four dimensions and N = 6 Chern-Simons matter theory (ABJM) in three dimensions. In N = 2 SCQCD we compute all possible four-point amplitudes at one loop and the two-loop amplitude with fundamental fields as external legs. In ABJM we extend the two-loop computation of four-point scattering amplitudes and of the Sudakov form factor beyond the planar limit. We also discuss our results in relation to the corresponding ones in N = 4 SYM, paying particular attention to the possible presence of dual conformal invariance and to maximum transcendentality.