DUALITIES AND EXACT RESULTS IN SUPERSYMMETRIC QFTS

In this thesis we analyze supersymmetric QFTs in three and four spacetime dimensions, with the goal of studying the infrared behavior of these theories. In Part I we analyze various dualities involving 3d N=2 theories with two tensor or adjoint fields and D-type superpotential. New dualities are discovered and we show relations between those and other 3d and 4d dualities. We also study 3d N=2 SQCD theories with orthogonal or symplectic gauge groups and monopole superpotential that exhibit s-confinement. These results are checked through the computation of the three-sphere partition function and via confinement/deconfinement procedures. In Part II we study exactly marginal deformations of 4d SCFTs and identify instances of theories that flow to different points of the same conformal manifold, a phenomenon denoted as conformal duality. We study a series of 4d N=1 theories engineered by a stack of D3-branes in Type IIB probing a Calabi-Yau toric singularity in the presence of an orientifold and build infinite families of pairs of conformally dual theories. In Part III we classify the 1-form symmetry groups of N=3 S-fold SCFTs as well as their global structures by analyzing the maximal refinements of their charge lattices. We study the charge lattices of S-folds and exceptional S-fold SCFTs of type E. We find that all but one of the exceptional S-folds do not admit a charge lattice consistent with the moduli space and must be discrete gaugings of free theories. We support this claim by developing constraints on the stratification of Coulomb branch and bounds for the 1-form symmetry group for a class of N=2 SCFTs.