Gauge Fixing of Superconformal Symmetries

In this chapter we combine the actions for vector multiplets and hypermultiplets, containing also compensating multiplets. We gauge fix the superconformal symmetries that are not necessary for the super-Poincare theory, and in such way obtain matter-coupled Poincare supergravity theories. We extensively discuss pure supergravity (using also other compensating multiplets leading to the off-shell theory) and discuss its reduction to \(\mathcal {N}=1\). Then we discuss appropriate variables for the gauge fixing of general matter couplings.