Warped Spectroscopy: Localization of Frozen Bulk Modes

TL;DR

This work analyzes dilaton-axion fluctuations in warped Type IIB flux compactifications, showing that the lightest mode tends to localize in long warped throats and acquire a mass near the warped string scale. By deriving a simplified 1D Schrödinger-like equation for the radial profile and estimating compensator effects, the authors demonstrate a regime-dependent hierarchy between flux-induced and KK scales, with the dilaton-axion generically needing integration out in deep throats but potentially remaining in the EFT in shorter throats. The results imply that the Gukov-Vafa-Witten superpotential remains relevant for localized modes but that warping can necessitate Kahler potential corrections and influence moduli stabilization, reheating, and brane-world phenomenology. Overall, the paper provides a tractable framework to understand localization, mass scales, and EFT validity in warped flux compactifications, highlighting when dilaton-axion dynamics can be neglected and when they must be included in 4D effective theories.

Abstract

We study the 10D equation of motion of dilaton-axion fluctuations in type IIB string compactifications with three-form flux, taking warping into account. Using simplified models with physics comparable to actual compactifications, we argue that the lightest mode localizes in long warped throats and takes a mass of order the warped string scale. Also, Gukov-Vafa-Witten superpotential is valid for the lightest mass mode; however, the mass is similar to the Kaluza-Klein scale, so the dilaton-axion should be integrated out of the effective theory in this long throat regime (leaving a constant superpotential). On the other hand, there is a large hierarchy between flux-induced and KK mass scales for moderate or weak warping. This hierarchy agrees with arguments given for trivial warping. Along the way, we also estimate the effect of the other 10D supergravity equations of motion on the dilaton-axion fluctuation, since these equations act as constraints. We argue that they give negligible corrections to the simplest approximation.