String Theory and Grand Unification Suggest a Sub-Microelectronvolt QCD Axion

TL;DR

This paper combines string theory and grand unification to constrain the QCD axion mass to a very light range, with implications for dark matter searches and the axiverse's structure.

Contribution

It provides new bounds on the QCD axion mass and axiverse complexity based on string compactifications and unification principles.

Findings

Axion mass likely between 10^{-11} eV and 10^{-8} eV.

Limits on the number of axions in the string axiverse (~47).

No axions found that explain recent dark energy hints with high decay constants.

Abstract

Axions, grand unification, and string theory are each compelling extensions of the Standard Model. We show that combining these frameworks imposes strong constraints on the QCD axion mass. Using unitarity arguments and explicit string compactifications - such as those from the Kreuzer-Skarke (KS) type IIB ensemble - we find that the axion mass is favored to lie within the range $10^{-11}$ eV $\lesssim m_a \lesssim$ $10^{-8}$ eV. This range is directly relevant for near-future axion dark matter searches, including ABRACADABRA/DMRadio and CASPEr. We argue that grand unification and the absence of proton decay suggest a compactification volume that keeps the string scale above the unification scale ($\sim$$10^{16}$ GeV), which in turn limits how heavy the axion can be. The same requirements limit the KS axiverse to have at most $\sim$47 axions. As an additional application of our methodology, we search for axions in the KS axiverse that could explain the recent Dark Energy Spectroscopic Instrument (DESI) hints of evolving dark energy but find none with high enough decay constant ($f_a \gtrsim 2.5 \times 10^{17}$ GeV); we comment on why such high decay constants and low axion masses are difficult to obtain in string compactifications more broadly.