An Intermediate Scale R-axion \& the QCD Axion

Abstract

An intermediate scale R-axion faces an immediate obstruction from the Dine-Festuccia-Komargodski (DFK) bound on the superpotential, $2|\langle W\rangle|\leq f_R F$, since for a nearly Minkowski vacuum it typically follows that $f_R\gtrsim M_{\rm Pl}$. We show that this lower bound on $f_R$ can be relaxed in an effective construction with the scalar potential tuned near zero via a mixed $F$- and $D$-term uplift, leading to a metastable vacuum in which the usual Planckian-$f_R$ inference from the DFK argument is avoided locally. Validity of the effective field theory and metastability of the small $f_R$ vacuum generically both imply a relaxed bound: $ f_R \gtrsim \sqrt{m_{3/2}M_{\rm Pl}} $. We also highlight that if the R-symmetry has a QCD anomaly, this potentially permits the R-axion to play the role of the QCD axion. TeV-scale supersymmetry permits $f_R\sim10^{11}$ GeV, this not only evades certain astrophysical and cosmological axion constraints, but notably lies in the window for which the observed dark matter abundance can be reproduced by the R-axion via the misalignment mechanism.