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

TL;DR

This paper demonstrates the equivalence between the superspace and component field approaches to four-dimensional N=1 conformal supergravity, providing detailed correspondences and analyzing gauge fixing procedures.

Contribution

It explicitly establishes the correspondence between superspace and component formulations of N=1 conformal supergravity, clarifying their relation and differences.

Findings

Explicit correspondence between superspace and component approaches

Analysis of curvature constraints and superconformal algebra

Comparison of gauge fixing procedures leading to Poincare supergravity

Abstract

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 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 Poincare supergravity since they look rather different between two approaches.