F-theory Axiverse

TL;DR

This work develops and analyzes three large ensembles of F-theory compactifications (Tree, Skeleton, K2) to study the phenomenology of Ramond-Ramond C$_4$ axions with up to $N=181{,}200$ species. By placing Kähler moduli in the $1$-stretched Kähler cone and modeling nonperturbative superpotential terms with leading prime-toric divisors, the authors compute axion masses, decay constants, and couplings to a proxy visible sector across geometries, revealing universal trends. A key finding is that axion decay constants $f$ decline as $h^{1,1}$ grows while axion–photon couplings $g_{\text{eff}}$ increase, leading to observational tensions for $h^{1,1}\gtrsim 10^4$ (helioscopes) and $h^{1,1}\gtrsim 5\times 10^3$ (X-ray spectra) under plausible UV assumptions. The results demonstrate that experimental axion-photon limits can probe substantial portions of the F-theory landscape, while highlighting the need for improved modeling of fluxes, Stückelberg masses, and fully realistic visible sectors.

Abstract

We compute the couplings of Ramond-Ramond four-form axions in three ensembles of F-theory compactifications, with up to 181,200 axions. We work in the stretched Kähler cone, where $α'$ corrections are plausibly controlled, and we use couplings to certain non-Abelian sectors as a proxy for couplings to photons. The axion masses, decay constants, and couplings to gauge sectors show striking universality across the ensembles. In particular, the axion-photon couplings grow with $h^{1,1}$, and models in our ensemble with $h^{1,1} \gtrsim$ 10,000 axions are in tension with helioscope constraints. Moreover, under mild assumptions about charged matter beyond the Standard Model, theories with $h^{1,1} \gtrsim$ 5,000 are in tension with Chandra measurements of X-ray spectra. This work is a first step toward understanding the phenomenology of quantum gravity theories with thousands of axions.

Figures (5)

• Figure 1: The effective axion-photon coupling $g_{\text{eff}}$ as a function of the number of axions, $h^{1,1}$. The points show the mean value, and the error bars show the standard deviation in each bin. Models above the CAST line are excluded, and models above the projected IAXO line could be tested or excluded. We have imposed $\alpha^{-1}_\text{EM, UV} \geq 19.5$, and applied a mass cut $m \le 10^{-2} \text{ eV}$ for comparison to helioscope experiments: see §\ref{['sec:methods']}. The K2 point is at $h^{1,1}=181{,}200$, and the largest $h^{1,1}$ shown here for the Skeleton ensemble is $h^{1,1}=8{,}955$.
• Figure 2: The mean values across different geometries of $\text{max} \log_{10}(f/M_\text{pl})$, $\text{median} \log_{10}(f/M_\text{pl})$, and $\text{min} \log_{10}(f/M_\text{pl})$ in the Kreuzer-Skarke, Tree, and Skeleton ensembles. The error bars show the standard deviation in each bin.
• Figure 3: Decay constants $f$ and the string scale $m_s$. Max, median, and min values are shown. The fits shown are taken to the data points with $\log_{10}(m_s/M_\text{pl}) \leq -3$.
• Figure 4: Axion masses as functions of $h^{1,1}$. The blue, green, and gray points are the mean axion masses in the Kreuzer-Skarke, Tree, and Skeleton ensembles, respectively, and the error bars are the standard deviation in each bin. The red points show the string mass $m_s$, and the fit in red to $\log_{10}(m_s/M_\text{pl})$ is given by $\log_{10}(m_s/M_\text{pl}) = -2.08 \log_{10}(h^{1,1}) - 0.07$ with $r^2 = 0.94$. Characteristic energy scales are labeled for reference.
• Figure 5: X-ray constraints on the effective axion-photon coupling $g_{\text{eff}}$. The error bars show the standard deviation in each bin. Models above the Chandra line are excluded, and models above the projected STROBE-X line could be tested or excluded. We have imposed $\alpha^{-1}_\text{EM, UV} \geq 29.5$, and applied a mass cut $m \le 10^{-12} \text{ eV}$.

Theorems & Definitions (5)

• Proposition 1
• Proposition 2
• Lemma 1
• Lemma 2
• Proposition 3