On effective action of string theory flux compactifications

TL;DR

This paper analyzes the effective four-dimensional actions derived from string theory flux compactifications, focusing on their consistency with ten-dimensional supergravity equations and the conditions under which agreement holds.

Contribution

It clarifies the conditions for the agreement between ten-dimensional supergravity and four-dimensional effective actions in flux compactifications, highlighting limitations when modes depend on-shell on the Kahler modulus.

Findings

Effective actions match ten-dimensional supergravity equations when evaluated on full solutions.

Discrepancies arise when effective actions are evaluated on on-shell modes depending on the Kahler modulus.

The analysis emphasizes the importance of mode dependence in deriving consistent effective theories.

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.