Warped Spectroscopy: Localization of Frozen Bulk Modes

TL;DR

This paper analyzes the localization and mass of dilaton-axion fluctuations in warped type IIB string compactifications, showing the lightest mode localizes in warped throats and justifies effective theory simplifications.

Contribution

It provides a detailed study of dilaton-axion modes in warped compactifications, confirming localization effects and the validity of superpotential approximations for the lightest mode.

Findings

Lightest mode localizes in long warped throats.

Mass of the lightest mode is of order the warped string scale.

Hierarchy between flux-induced and KK masses is consistent with trivial warping arguments.

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.