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

## TL;DR

This paper presents a method for reducing four-dimensional conformal supergravity from N=2 to N=1 supersymmetry while maintaining off-shell structures, simplifying the process and clarifying the resulting N=1 superconformal symmetry.

## Contribution

It introduces an off-shell reduction procedure from N=2 to N=1 conformal supergravity, simplifying the process compared to previous methods and clarifying the symmetry correspondence.

## Key findings

- Off-shell N=2 to N=1 reduction is achieved by truncating the gravitino multiplet.
- The reduction process simplifies the correspondence to standard N=1 conformal supergravity.
- The reduced N=1 supergravity action is explicitly derived.

## Abstract

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