In this project we will search for non –trivial dualities between theories in 3 –dimensional and 4-dimensional Quantum Field Theories, which play a key role in the study of strongly correlated systems. This has important implications for both Particle and Condensed Matter physics. In order to achieve this task, we will make use for several non-perturbative techniques, such as localization and AdSCFT, togheter with derivations from well known situations Supersymmetric theories.