Effective Potentials for Light Moduli

TL;DR

The paper questions the consistency of the KKLT moduli-stabilization approach by showing that integrating out heavy moduli and then adding a non-perturbative term to the superpotential is not self-consistent, because non-perturbative effects modify the underlying Kaehler-invariant function. By deriving a corrected effective potential for the Kaehler modulus $T$ that includes terms like $c\,C^{2}e^{-2aT}$ and $|C|^{2}e^{-a(T+\bar T)}$, it demonstrates that metastable de Sitter vacua can arise without uplifting in certain setups. While KKLT’s basic claim that non-perturbative effects stabilize Kaehler moduli remains, the full potential alters the cosmological implications and requires revisiting prior conclusions, including the role of perturbative corrections to the Kaehler potential. The work underscores the need for a holistic treatment of heavy-moduli integration and non-perturbative corrections in flux compactifications.

Abstract

We examine recent work on compactifications of string theory with fluxes, where effective potentials for light moduli have been derived after integrating out moduli that are assumed to be heavy at the classical level, and then adding non-perturbative (NP) corrections to the superpotential. We find that this two stage procedure is not valid and that the correct potential has additional terms. Althought this does not affect the conclusion of Kachru et al (KKLT) that the Kaehler moduli may be stabilized by NP effects, it can affect the detailed physics. In particular it is possible to get metastable dS minima without adding uplifting terms.