Constraining F-theory Model Building with QCD Axions

TL;DR

This paper explores QCD axion physics within 4D F-theory MSSM models, deriving couplings and potentials from string theory, and constraining the model parameters based on geometric and physical considerations.

Contribution

It provides the first detailed top-down analysis of QCD axions in F-theory MSSM models, including geometric constraints and axion property estimates.

Findings

Derived axion coupling terms and potentials from string theory.

Identified constraints on the Kähler moduli space from physical and geometric criteria.

Estimated typical QCD axion mass around 10^{-9} eV and decay constant near 10^{15} GeV.

Abstract

In this paper, we investigate axion physics in 4D F-theory MSSM models. We derive the axion coupling term with QCD gauge fields and the axion potential from a top-down perspective, from both IIB superstring and the dual M-theory picture. For the explicit geometric model, we employ the "quadrillion" landscape of 4D F-theory models with the exact Standard Model chiral spectrum, and study simple base threefolds such as $\mathbb{P}^3$, $\mathbb{P}^1\times\mathbb{P}^2$, the generalized Hirzebruch threefold $\tilde{\mathbb{F}}_3$ and $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1$. We derive exclusion constraints on the K\"ahler moduli space of the base threefold from the CP violation angle, the Standard Model gauge coupling constants and the stretched K\"{a}hler cone condition. We find stringent constraints on the set of base divisors that should be rigid or rigidified by the inclusion of flux. For the allowed regions of the parameter space, we estimate the typical mass of detectable QCD axions to be around $10^{-9}$eV, and the axion decay constant to be around $f_a\sim 10^{15}$GeV.