$\mathcal{N}=2$ Supersymmetric Actions

In this note we discuss $\mathcal{N}=2$ gauge and matter actions in the UV build out of $\mathcal{N}=1$ actions with appropriate coefficients between terms in the Lagrangian to account for the $SU(2)_R$ R-symmetry. The $\mathcal{N}=1$ actions are given in the formalism of superspace and superfields. We also discuss supersymmetric vacua and give definitions of the Coloumb and Higgs branches. We discuss briefly the BPS mass bound. Finally, we discuss low energy effective actions in the IR and argue that the Kahler potential, should in fact be special Kahler given in terms of a prepotential.