Higher-Derivative Supergravity and Moduli Stabilization

TL;DR

This paper shows that ghost-free four-derivative operators in $\mathcal{N}=1$ SUSY and supergravity yield a cubic auxiliary-field equation, reducing to a single analytic, EFT-consistent on-shell theory that corrects the scalar potential. It then connects these four-derivative terms to Type IIB Calabi–Yau orientifold compactifications, demonstrating a new perturbative moduli-stabilization mechanism driven by $\alpha'^3 R^4$-induced effects, with a model-independent AdS minimum for $\chi(M_3)>0$ when the new correction has negative sign. The analysis combines global and local SUSY, Wess–Zumino and O'Raifeartaigh-type models to illuminate the fate of flat directions under higher-derivative corrections and computes the four-derivative terms arising from ten-dimensional $R^4$ reductions, including their impact on the Kähler-moduli sector. Overall, the results provide a controlled, EFT-consistent route to stabilizing Calabi–Yau moduli via perturbative corrections, while outlining key open issues like the sign determination of the higher-derivative coupling and the role of warping.

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 $(α')^3 R^4$ corrections in ten dimensions for the respective $\mathcal{N}=1$ Kähler moduli sector. We prove that together with flux and the known $(α')^3$-corrections the higher-derivative term stabilizes all Calabi-Yau manifolds with positive Euler number, provided the sign of the new correction is negative.