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In $D=4$, $\cal{N}=1$ conformal superspace, the Yang-Mills matter coupledsupergravity system is constructed where the Yang-Mills gauge interaction isintroduced by extending the superconformal group to include the K\"ahlerisometry group of chiral matter fields. There are two gauge-fixing proceduresto get to the component Poincar\'e supergravity: one via the superconformalcomponent formalism and the other via the Poincar\'e superspace formalism.These two types of superconformal gauge-fixing conditions are analyzed indetail and their correspondence is clarified.

Superspace Gauge Fixing in Yang-Mills Matter Coupled Conformal Supergravity