Component versus superspace approaches to D = 4, N = 1 conformal supergravity

The superspace formulation of N = 1 conformal supergravity in four dimensions is demonstrated to be equivalent to the conventional component field approach based on the superconformal tensor calculus. The detailed correspondence between the two approaches is explicitly given for various quantities: superconformal gauge fields, curvatures and curvature constraints, general conformal multiplets and their transformation laws, and so on. In particular, we carefully analyze the curvature constraints leading to the superconformal algebra and also the superconformal gauge fixing leading to Poincaré supergravity, since they look rather different between the two approaches.