Higher-Derivative Supergravity and Moduli Stabilization

TL;DR

This paper reviews ghost-free higher-derivative terms in supergravity, analyzes their effects on moduli stabilization, and explicitly computes these corrections in type IIB string compactifications, demonstrating stabilization of certain Calabi-Yau manifolds.

Contribution

It provides a detailed analysis of higher-derivative supergravity terms and their role in stabilizing moduli in string compactifications, including explicit calculations for type IIB flux compactifications.

Findings

Higher-derivative terms induce cubic equations for auxiliary fields.

Only one solution is consistent with effective field theory.

Higher-derivative corrections stabilize all Calabi-Yau manifolds with positive Euler number.

Abstract

We review the ghost-free four-derivative terms for chiral superfields in $\mathcal{N}=1$ supersymmetry and supergravity. These terms induce cubic polynomial equations of motion for the chiral auxiliary fields and correct the scalar potential. We discuss the different solutions and argue that only one of them is consistent with the principles of effective field theory. Special attention is paid to the corrections along flat directions which can be stabilized or destabilized by the higher-derivative terms. We then compute these higher-derivative terms explicitly for the type IIB string compactified on a Calabi-Yau orientifold with fluxes via Kaluza-Klein reducing the $(\alpha')^3 R^4$ corrections in ten dimensions for the respective $\mathcal{N}=1$ K\"{a}hler moduli sector. We prove that together with flux and the known $(\alpha')^3$-corrections the higher-derivative term stabilizes all Calabi-Yau manifolds with positive Euler number, provided the sign of the new correction is negative.