Scalar Potential from Higher Derivative $\mathcal{N} = 1$ Superspace

TL;DR

This paper systematically studies how higher-derivative operators in $ abla=1$ supersymmetric theories modify scalar potentials, providing classifications, computational tools, and implications for string compactifications and moduli stabilization.

Contribution

It classifies superspace derivative operators affecting scalar potentials in $ abla=1$ supersymmetry and presents an algorithm for simplifying on-shell action computations.

Findings

Classified leading and next-to-leading order superspace derivative operators.

Developed an algorithm for on-shell action computation.

Analyzed supersymmetric vacua and corrections to no-scale models.

Abstract

The supersymmetric completion of higher-derivative operators often requires introducing corrections to the scalar potential. In this paper we study these corrections systematically in the context of theories with $\mathcal{N}=1$ global and local supersymmetry in $D=4$ focusing on ungauged chiral multiplets. In globally supersymmetric theories the most general off-shell effective scalar potential can be captured by a dependence of the K\"{a}hler potential on additional chiral superfields. For supergravity we find a much richer structure of possible corrections. In this context we classify the leading order and next-to-leading order superspace derivative operators and determine the component forms of a subclass thereof. Moreover, we present an algorithm that simplifies the computation of the respective on-shell action. As particular applications we study the structure of the supersymmetric vacua for these theories and comment on the form of the corrections to shift-symmetric no-scale models. These results are relevant for the computation of effective actions for string compactifications and, in turn, for moduli stabilization and string inflation.