$\mathcal{N} =1$ Supergravity in 4 Dimensions

Abstract

In this chapter we will study $\mathcal{N}=1$ supergravity in 4 dimensions. Supergravity can be defined as a supersymmetric theory of gravity, or otherwise as a theory of local supersymmetry. In practice, we will use a bit of both definitions to find it. Before that however, we need to define what supersymmetry is. After that, we will count degrees of freedom, in order to see what supergravity models we can have. After defining the vielbein-spin connection formulation of gravity, within which supergravity is defined, we will finally define the model of $\mathcal{N}=1$ supergravity.