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The superspace formulation of N=1 conformal supergravity in four dimensionsis demonstrated to be equivalent to the conventional component field approachbased on the superconformal tensor calculus. The detailed correspondencebetween two approaches is explicitly given for various quantities;superconformal gauge fields, curvatures and curvature constraints, generalconformal multiplets and their transformation laws, and so on. In particular,we carefully analyze the curvature constraints leading to the superconformalalgebra and also the superconformal gauge fixing leading to Poincaresupergravity since they look rather different between two approaches.

Component versus Superspace Approaches to D=4, N=1 Conformal Supergravity