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

39 pages

Cited by in corpus (7)

• New Fayet-Iliopoulos terms in $\mathcal{N}=2$ supergravity
• Topological couplings in higher derivative extensions of supersymmetric three-form gauge theories
• Constraining Liberated Supergravity
• Dual formulations of vortex strings in supersymmetric Abelian Higgs model
• Super Heat Kernel of General Second Order Operators in $N=1$ Superspace and One-Loop Divergence of Dilaton-coupled SYM Theory
• Super Heat Kernel and One-Loop Divergence of Super Yang-Mills Theory in Conformal Supergravity
• Component Actions of Liberated $\mathcal{N}=1$ Supergravity and New Fayet-Iliopoulos Terms in Superconformal Tensor Calculus