Supergravity for Effective Theories

TL;DR

This paper develops a formalism for coupling higher-derivative supersymmetric effective field theories to supergravity, enabling consistent component actions and applications to inflation models.

Contribution

It introduces a comprehensive toolkit for coupling supersymmetric effective theories with higher derivatives to supergravity, including explicit action construction methods.

Findings

Component actions match linearized Ferrara-Zumino multiplet expectations.

Formalism applied to inflation effective theory in a companion paper.

Framework accommodates arbitrary derivatives and curvature couplings.

Abstract

Higher-derivative operators are central elements of any effective field theory. In supersymmetric theories, these operators include terms with derivatives in the K\"ahler potential. We develop a toolkit for coupling such supersymmetric effective field theories to supergravity. We explain how to write the action for minimal supergravity coupled to chiral superfields with arbitrary numbers of derivatives and curvature couplings. We discuss two examples in detail, showing how the component actions agree with the expectations from the linearized description in terms of a Ferrara-Zumino multiplet. In a companion paper, we apply the formalism to the effective theory of inflation.