Component Actions from Curved Superspace: Normal Coordinates and Ectoplasm

TL;DR

This paper introduces efficient superspace techniques for deriving component actions in supergravity-matter systems, utilizing normal coordinates and differential forms to simplify calculations across various superspaces.

Contribution

It presents two novel methods—normal coordinate expansion and differential form interpretation—for deriving component actions in supergravity coupled to matter.

Findings

Normal coordinate method simplifies covariant expansion of superfield actions.

Differential form approach provides straightforward derivation of component Lagrangians.

Applicable to a wide range of superspace formulations.

Abstract

We give efficient superspace methods for deriving component actions for supergravity coupled to matter. One method uses normal coordinates to covariantly expand the superfield action, and can be applied straightforwardly to any superspace. The other interprets the component lagrangian as a differential form on a bosonic hypersurface in superspace, and gives a simple derivation for pertinent cases such as chiral superspace.