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We discuss $N=2\to N=1$ reduction in four dimensional conformal supergravity.In particular, we keep the off-shell structure of supermultiplets (excepthypermultiplets). As we will show, starting with (almost) off-shell conformalsupergravity makes the procedure simpler than that from $N=2$ Poincar\'esupergravity, which makes it easier to show the correspondence to the standard$N=1$ conformal supergravity. We find that the $N=1$ superconformal symmetry issimply realized by truncating the gravitino multiplet. We also discuss theconsistency with the original $N=2$ system and show the reduced $N=1$ conformalsupergravity action.

Off-shell $N=2\to N=1$ reduction in 4D conformal supergravity