On conformal supergravity and projective superspace

TL;DR

This paper extends the projective superspace formulation of N=2 supergravity by providing explicit details for Howe's realization, which involves a different tangent space group and super-Weyl transformation parameters.

Contribution

It offers a detailed extension of the projective superspace formulation to Howe's N=2 conformal supergravity with explicit construction.

Findings

Explicit formulation of Howe's realization of N=2 conformal supergravity.

Clarification of super-Weyl transformation parameters.

Extension of superspace techniques to new supergravity models.

Abstract

The projective superspace formulation for four-dimensional N = 2 matter-coupled supergravity presented in arXiv:0805.4683 makes use of the variant superspace realization for the N = 2 Weyl multiplet in which the structure group is SL(2,C) x SU(2) and the super-Weyl transformations are generated by a covariantly chiral parameter. An extension to Howe's realization of N = 2 conformal supergravity in which the tangent space group is SL(2,C) x U(2) and the super-Weyl transformations are generated by a real unconstrained parameter was briefly sketched. Here we give the explicit details of the extension.