PQ Axiverse

TL;DR

This paper demonstrates that the strong CP problem can be resolved within a broad class of string theory compactifications by analyzing quantum gravitational effects, instanton contributions, and cosmological constraints, highlighting the role of large N effects.

Contribution

It provides a detailed analysis of how flux compactifications and large N effects suppress CP-violating contributions, offering a string-theoretic solution to the strong CP problem.

Findings

D-brane instanton contributions to neutron EDM are negligible for N>17.

Large N effects create hierarchies that suppress instanton actions and ultraviolet cutoff.

A significant fraction of models satisfy cosmological and astrophysical constraints.

Abstract

We show that the strong CP problem is solved in a large class of compactifications of string theory. The Peccei-Quinn mechanism solves the strong CP problem if the CP-breaking effects of the ultraviolet completion of gravity and of QCD are small compared to the CP-preserving axion potential generated by low-energy QCD instantons. We characterize both classes of effects. To understand quantum gravitational effects, we consider an ensemble of flux compactifications of type IIB string theory on orientifolds of Calabi-Yau hypersurfaces in the geometric regime, taking a simple model of QCD on D7-branes. We show that the D-brane instanton contribution to the neutron electric dipole moment falls exponentially in $N^4$, with $N$ the number of axions. In particular, this contribution is negligible in all models in our ensemble with $N>17$. We interpret this result as a consequence of large $N$ effects in the geometry that create hierarchies in instanton actions and also suppress the ultraviolet cutoff. We also compute the CP breaking due to high-energy instantons in QCD. In the absence of vectorlike pairs, we find contributions to the neutron electric dipole moment that are not excluded, but that could be accessible to future experiments if the scale of supersymmetry breaking is sufficiently low. The existence of vectorlike pairs can lead to a larger dipole moment. Finally, we show that a significant fraction of models are allowed by standard cosmological and astrophysical constraints.