Dynamics of warped compactifications and the shape of the warped landscape

TL;DR

This paper investigates warped compactifications in string theory, deriving a four-dimensional potential, analyzing moduli stabilization, and exploring implications for de Sitter vacua, inflation, and the effective action with mobile branes.

Contribution

It provides a general formula for the 4D potential from 10D quantities, introduces the slope-dominance criterion, and analyzes moduli and brane dynamics in warped compactifications.

Findings

Derived a systematic 4D potential formula for warped compactifications.

Identified conditions to evade no-go theorems for de Sitter vacua.

Analyzed scalar perturbations revealing new features of moduli and kinetic terms.

Abstract

The dynamics of warped/flux compactifications is studied, including warping effects, providing a firmer footing for investigation of the "landscape." We present a general formula for the four-dimensional potential of warped compactifications in terms of ten-dimensional quantities. This allows a systematic investigation of moduli-fixing effects and potentials for mobile branes. We provide a necessary criterion, "slope-dominance," for evading "no-go" results for de Sitter vacua. We outline the ten-dimensional derivation of the non-perturbative effects that should accomplish this in KKLT examples, and outline a systematic discussion of their corrections. We show that potentials for mobile branes receive generic contributions inhibiting slow-roll inflation. We give a linearized analysis of general scalar perturbations of warped IIB compactifications, revealing new features for both time independent and dependent moduli, and new aspects of the kinetic part of the four-dimensional effective action. The universal Kahler modulus is found_not_ to be a simple scaling of the internal metric, and a prescription is given for defining holomorphic Kahler moduli, including warping effects. In the presence of mobile branes, this prescription elucidates couplings between bulk and brane fields. Our results are thus relevant to investigations of the existence of de Sitter vacua in string theory, and of their phenomenology, cosmology, and statistics.