4D N = 2 Supergravity and Projective Superspace

TL;DR

This paper develops a projective superspace formulation for 4D N=2 supergravity, introducing new off-shell multiplets and an invariant action principle, advancing the understanding of matter coupling in supergravity theories.

Contribution

It introduces a novel variant superspace realization for the N=2 Weyl multiplet and constructs off-shell supermultiplets and actions in this framework.

Findings

New superspace realization for N=2 Weyl multiplet

Construction of off-shell matter multiplets in curved superspace

Development of a super-Weyl invariant action principle

Abstract

This paper presents a projective superspace formulation for 4D N = 2 matter-coupled supergravity. We first describe a variant superspace realization for the N = 2 Weyl multiplet. It differs from that proposed by Howe in 1982 by the choice of the structure group (SO(3,1) x SU(2) versus SO(3,1) x U(2)), which implies that the super-Weyl transformations are generated by a covariantly chiral parameter instead of a real unconstrained one. We introduce various off-shell supermultiplets which are curved superspace analogues of the superconformal projective multiplets in global supersymmetry and which describe matter fields coupled to supergravity. A manifestly locally supersymmetric and super-Weyl invariant action principle is given. Off-shell locally supersymmetric nonlinear sigma models are presented in this new superspace.