Supergravity for Effective Theories

TL;DR

The paper develops a comprehensive toolkit for coupling higher-derivative supersymmetric EFTs to minimal supergravity, combining curved superspace techniques with a systematic component expansion. It shows how to construct invariant actions with higher-derivative Kähler potentials and verifies consistency with linearized Ferrara-Zumino multiplet couplings, including improvements and curvature terms. The formalism is then applied to a supersymmetric EFT of inflation, revealing curvature-induced contributions to the inflaton partner’s mass and notable effects for small sound speed c_s. These results lay groundwork for analyzing a broad class of SUSY EFTs in curved backgrounds, with detailed inflationary applications reserved for a companion paper.

Abstract

Higher-derivative operators are central elements of any effective field theory. In supersymmetric theories, these operators include terms with derivatives in the Kähler 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.