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String theory and grand unification suggest a submicroelectronvolt QCD axion

Joshua N. Benabou1,2, Katherine Fraser1,2, Mario Reig3, and Benjamin R. Safdi1,2

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Phys. Rev. D 112, 066003 – Published 9 September, 2025

DOI: https://doi.org/10.1103/lthr-97lm

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 perturbative 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≲ma≲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 (∼1016  GeV), which in turn limits how heavy the axion can be. The same requirements limit the KS axiverse to have at most ∼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 hints of evolving dark energy but find none with high enough decay constant (fa≳2.5×1017  GeV); we comment on why such high decay constants and low axion masses are difficult to obtain in string compactifications more broadly.

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Phys. Rev. D 112, 066003– Published 9 September, 2025
  • Received 1 June 2025
  • Accepted 13 August 2025
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