Testing F-theory GUTs with the Axiverse

Abstract

We show that axions coupled to photons in F-theory Grand Unified Theories (GUTs) satisfy the coupling-to-mass relation $g_{a\gamma}/m_a \leq C\, \frac{\alpha_{\rm em}}{2\pi}\frac{1}{m_\pi f_\pi}$, with $C$ a calculable coefficient. This bound is saturated for the QCD axion with $C = \mathcal{O}(1)$ and holds in field theoretic and perturbative heterotic GUT constructions. In F-theory, topological GUT symmetry breaking by hypercharge flux introduces axion-like particles (ALPs) coupled to photons without coupling to QCD. These ALPs arise from the non-universal holomorphic threshold corrections to the gauge kinetic functions induced by the hypercharge flux. When gauge couplings approximately unify near the string scale, as required in phenomenologically viable models, the shift symmetries of these ALPs are broken by D-instantons whose action is controlled by the size of the threshold corrections to the gauge couplings. Small corrections imply unsuppressed instantons and heavy ALPs. We compute the resulting axion potentials and show that the coupling-to-mass ratio $g_{a\gamma}/m_a$ for every non-universal ALP lies well below the QCD axion prediction. We consider possible loopholes to this result -- some of which could lead to $C\gg 1$ -- and argue that none of them allows for $g_{a\gamma}/m_a$ to be arbitrarily above the QCD axion prediction within regions of control for the effective action. The bound persists in models with large threshold corrections, where new incomplete GUT multiplets at intermediate energy scales are required. As a result, in the geometric regime, where the $\alpha'$ expansion is under control, no ALP parametrically above the QCD axion band exists. Our results make F-theory GUTs falsifiable: finding an ALP far above the QCD band, for example discovering axion-induced cosmic birefringence, rules out F-theory GUTs in regimes of control of the effective theory.