Aspects of Supersymmetry: Duality, Enhancement, and (Super)-Power of Deconfinement

This thesis is devoted to the study of different non-perturbative aspects of supersymmetric quantum field theory (SQFT). We analyze SQFTs living in different space-time dimensions and preserving different number of supercharges but with a special emphasis to the minimally supersymmetric theories in $4d$ ($\cN=1$). In the first part of this thesis, we generalize a technique called sequential deconfinement allowing us to prove various $4d \, \cN=1$ infrared (IR) dualities by iterative use of more fundamental ones. It includes all the S-confining dualities, meaning gauge theories dual to a Wess-Zumino model, with simple gauge group, vanishing superpotential and matter fields transforming in rank-1 and/or rank-2 representations. As well as the self-duality of the $4d \, \cN=1$ $USp(2N)$ gauge theory with an antisymmetric field and 8 fundamentals. In the second part, we consider $5d$ KK-dualities, that is multiple $5d$ gauge theories with the same $6d$ infinite coupling limit. Then we use these KK-theories to construct new non-trivial $4d \, \cN=1$ IR dualities. In the last part, we propose new classes of $4d \, \cN=1$ S-confining gauge theories and discuss some $3d$ reductions. These $3d$ S-confining theories provide an understanding of a recently proposed $4d \, \cN=1$ theory that flows to the same conformal manifold of $\cN=4$ super Yang-Mills with $SU(2N+1)$ gauge group. The $3d$ perspective allows us to generalize the construction by providing another example of a flow with supersymmetry enhancement.