The Dimensional Reduction and Kähler Metric of Forms In Flux and Warping

TL;DR

This paper derives a first-principles 4D moduli-space metric for axion-like moduli in IIB flux compactifications with ISD flux on conformally CY manifolds, showing that warping and flux alter the Kähler metric even at the classical level. By solving the 10D gauge/diffeomorphism constraints and performing a careful dimensional reduction with compensators, the authors obtain both the kinetic terms and holomorphic variables that define the corrected Kähler potential. In simple cases, the corrections scale as the compactification volume to the power $-2/3$, and in torus-factor backgrounds the moduli space remains protected by metric formality. The results have broad implications for nonperturbative moduli stabilization, cosmology, and inflation in warped flux compactifications, and they clarify the limitations of inferring 4D physics solely from CY topology.

Abstract

We present a first-principles derivation of the Kähler metric for axion-like moduli of conformally Calabi-Yau compactifications of IIB string theory with imaginary self-dual 3-form flux at the classical level. We find that the warp factor and flux modify the moduli space metric and therefore Kähler potential even in classical supergravity, with the modifications scaling as (volume)$^{-2/3}$ in the large-volume limit. Our derivation emphasizes the role of constraints from 10D gauge symmetries and highlights metric formality as a geometric property that protects the moduli space of highly supersymmetric toroidal orientifolds. Our results have important quantitative implications for nonperturbative moduli stabilization, phenomenology, and cosmology in flux compactifications.