Dimensional Reduction and K\"ahler Metric for Metric Moduli in Imaginary Self-Dual Flux

TL;DR

This paper derives the 4D effective field theory for geometric moduli in warped Calabi-Yau compactifications of type IIB string theory with flux, providing new insights into moduli space metrics and flat directions.

Contribution

It provides the first-principles derivation of the Kähler moduli space metric and an effective action for complex structure flat directions in flux compactifications.

Findings

Derived the metric on Kähler moduli space from 10D equations of motion.

Established an effective action for complex structure flat directions.

Presented explicit examples in toroidal compactifications.

Abstract

Understanding which effective field theories are consistent with an ultraviolet completion in quantum gravity is an important theoretical question. Therefore, it is important to know the structure of the 4D effective theory associated with a given compactification of string theory. We present a first-principles derivation of the low-energy 4D effective theory of geometric moduli in a warped Calabi-Yau compactification of type IIB string theory with imaginary self-dual 3-form flux. This completes the derivation of the metric on K\"ahler moduli space from the 10D equations of motion. We also give the first derivation of an effective action for flat directions in the complex structure moduli space of the Calabi-Yau (which generically mix with the axiodilaton) and work out explicit examples of complex structure flat directions in toroidal compactifications. Finally, we outline applications to a variety of settings, including precision string phenomenology and the tadpole conjecture.