On effective action of string theory flux compactifications

TL;DR

The paper analyzes when four-dimensional effective actions for string theory flux compactifications reliably reproduce ten-dimensional supergravity dynamics. By comparing a soluble higher-dimensional toy model and explicit Type IIB flux compactifications with localized sources, it shows that the full off-shell potential must be used to ensure equivalence with the 10D equations; evaluating the 4D action on a subset of on-shell modes depending on the Kähler modulus can break this correspondence. The results clarify how the overall Kähler modulus interacts with brane and flux contributions, describe the proper form of the 4D potential ${\cal V}(\sigma)$, and lay out constraints on obtaining de Sitter vacua in this framework, including the role of non-ISD fluxes and uplift mechanisms. These insights have implications for KKLT-type constructions and the backreaction of localized sources in warped flux compactifications.

Abstract

We discuss four dimensional effective actions of string theory flux compactifications. These effective actions describe four dimensional gravity coupled to overall Kahler modulus of the compactification manifold. We demonstrate the agreement between ten dimensional equations of motion of supergravity with localized branes, and equations of motion derived from the effective action. The agreement is lost however if one evaluates the full effective action on the equations of motion for a subset of the supergravity modes, provided these modes depend on-shell on the Kahler modulus.