Supersymmetry (SUSY) is a symmetry which combines fermions and bosons into the same multiplets. It plays a crucial role in the structure of string theory, and in fact its first appearance as a symmetry in physics arose in trying to extend the bosonic string to include fermions. In string theory, SUSY guarantees the absence of divergences and of tachyonic scalars. Moreover, as discussed in Section 1.3.3, the simplest version of supersymmetry in four dimensions may provide a perturbative solution to the electroweak hierarchy problem, and thus is key to many proposals for physics beyond the Standard Model. For these reasons, most 4d string theory compactifications studied to date are supersymmetric, and lead to SUSY effective theories at low energies.

In this chapter we review general results for 4d N = 1 SUSY and describe its possible role in stabilizing the electroweak scale against radiative corrections. We review local supersymmetry, which leads to the inclusion of gravitation and gives rise to 4d N = 1 supergravity, which may play an important phenomenological role by mediating SUSY breaking. We also introduce the simplest SUSY extension of the SM, the Minimal Supersymmetric Standard Model (MSSM), for reference in future chapters. In addition, we provide a brief introduction to extended SUSY, which includes additional supersymmetry generators; although not of direct interest for particle physics, extended SUSY plays an important role in string theory, and actually appears in intermediate steps in explicit phenomenologically interesting string constructions.