The QCD Axion and Moduli Stabilisation

TL;DR

This paper explores conditions for the coexistence of a QCD axion with stabilized moduli in string theory, identifying challenges with traditional approaches and proposing solutions for realistic axion decay constants.

Contribution

It presents a no-go theorem for supersymmetric moduli stabilization with unfixed axions and demonstrates how non-supersymmetric stabilization can achieve viable axion decay constants.

Findings

Traditional moduli stabilization yields too large axion masses.

A no-go theorem applies to supersymmetric stabilization with unfixed axions.

Non-supersymmetric stabilization can produce acceptable axion decay constants.

Abstract

We investigate the conditions for a QCD axion to coexist with stabilised moduli in string compactifications. We show how the simplest approaches to moduli stabilisation give unacceptably large masses to the axions. We observe that solving the F-term equations is insufficient for realistic moduli stabilisation and give a no-go theorem on supersymmetric moduli stabilisation with unfixed axions applicable to all string compactifications and relevant to much current work. We demonstrate how nonsupersymmetric moduli stabilisation with unfixed axions can be realised. We finally outline how to stabilise the moduli such that f_a is within the allowed window 10^9 GeV < f_a < 10^{12} GeV, with f_a ~ \sqrt{M_{SUSY} M_P}.