Symmetries of curved superspace

TL;DR

This paper reviews and extends the formalism for determining supersymmetric isometries in curved superspace, providing a universal framework applicable to various supergravity theories and recent background constructions.

Contribution

It demonstrates how to extract recent results on supersymmetric backgrounds from the superspace formalism and introduces a universal superspace approach for off-shell N=1 supergravity backgrounds.

Findings

Unified superspace method for supersymmetric backgrounds

Connection between different supergravity formulations

Applicability to various off-shell supergravity theories

Abstract

The formalism to determine (conformal) isometries of a given curved superspace was elaborated almost two decades ago in the context of the old minimal formulation for N=1 supergravity in four dimensions (4D). This formalism is universal, for it may readily be generalized to supersymmetric backgrounds associated with any supergravity theory formulated in superspace. In particular, it has already been used to construct rigid supersymmetric field theories in 5D N=1, 4D N=2 and 3D (p,q) anti-de Sitter superspaces. In the last two years, there have appeared a number of publications devoted to the construction of supersymmetric backgrounds in off-shell 4D N=1 supergravity theories using component field considerations. Here we demonstrate how to read off the key results of these recent publications from the more general superspace approach developed in the 1990s. We also present a universal superspace setting to construct supersymmetric backgrounds, which is applicable to any of the known off-shell formulations for N=1 supergravity. This approach is based on the realizations of the new minimal and non-minimal supergravity theories as super-Weyl invariant couplings of the old minimal supergravity to certain conformal compensators.