The $F$-term Problem and other Challenges of Stringy Quintessence

TL;DR

This paper analyzes string-theoretic quintessence models, highlighting challenges like the light volume problem and an $F$-term problem, and discusses the difficulties in achieving stable, slow-roll de Sitter vacua within known string compactifications.

Contribution

It identifies and discusses key theoretical challenges in realizing string-based quintessence models, including the light volume and $F$-term problems, and explores implications for de Sitter vacua.

Findings

Large-volume type-IIB flux compactifications are preferred.

The volume modulus tends to remain too light, causing the 'light volume problem'.

Positive energy from SUSY breaking exceeds negative contributions, leading to the '$F$-term problem'.

Abstract

We attempt a systematic analysis of string-theoretic quintessence models as an alternative to metastable de Sitter vacua. It appears that, within the boundaries of what is known, large-volume type-IIB flux compactifications are preferred. Here the quintessence scalar is the ratio of certain 4-cycle volumes. It has already been noticed that the volume modulus, which must be stabilized, tends to remain too light. One may call this the "light volume problem". In addition, we identify an "$F$-term problem": The positive energy density of standard-model SUSY breaking is higher than the depth of all known negative contributions. We discuss what it would take to resolve these issues and comment on partially related challenges for axionic quintessence. In particular, large cancellations between positive and negative potential terms appear unavoidable in general. As a further challenge, one should then explain why a small de-tuning cannot be used to uplift into a deep slow-roll regime, violating de Sitter swampland conjectures.