On Potentials from Fluxes

TL;DR

The paper investigates how fluxes in type IIB compactifications generate potentials for moduli and how this interacts with the no-go theorem for de Sitter space. Through a D-dimensional flux-compactification analysis and a detailed examination of the GKP setup, it shows that a positive potential for some moduli can emerge only when the volume modulus is not stabilized at a fixed point, and that a nontrivial warp factor necessitates including the entire KK spectrum, preventing a simple 4D potential derivation. The work clarifies that, in general, fluxes alone yield a negative-definite potential for the volume modulus unless nonperturbative effects (e.g., racetrack scenarios) or other stabilization mechanisms are invoked, with significant implications for constructing de Sitter vacua and for moduli stabilization in string compactifications.

Abstract

We discuss the compactification of type IIB supergravity with fluxes to generate a potential for the moduli. In particular we resolve an apparent conflict with the no-go theorem for de Sitter space. It is shown that a positive potential for certain moduli is possible in situations where the volume modulus has no critical point. We also point out that the derivation of the potential is strictly valid only for a trivial warp factor. To go beyond that seems to require the inclusion of all the Kaluza-Klein excitations. We end with a discussion of the stabilization of the volume modulus.