A QCD R-Axion

TL;DR

The paper investigates identifying the Peccei–Quinn symmetry with the R-symmetry in supersymmetric extensions of the Standard Model, proposing generalized R-charge assignments and intermediate-scale R-breaking to yield an R-axion that acts as the QCD axion. It develops explicit model-building frameworks where the μ-term is forbidden by R-symmetry and generated via a Kim–Nilles-type mechanism, with spontaneous R-breaking setting the PQ scale $f_a \\sim \sqrt{m_{soft}M_{Pl}}$ and $f_a \sim 10^{11}$ GeV. A central challenge—the axion quality problem from explicit R-breaking—is addressed by embedding the R-symmetry into a gauged U(1) via the Green–Schwarz mechanism, which also yields a viable UV completion, field-dependent FI terms, and potential Dirac gaugino masses. The work analyzes the resulting anomaly constraints, D-term bounds, and proton-decay suppression, and discusses rich phenomenology including metastable LSPs and axion/electroweak interplay, with open avenues for UV completions and cosmological implications. Overall, the proposal offers a coherent route to a UV-complete, R-symmetric solution to the strong CP problem that integrates axion physics with Dirac gauginos and a consistent SUSY-breaking structure.

Abstract

R-parity can be extended to a continuous global U(1)${}_R$ symmetry. We investigate whether an anomalous U(1)${}_R$ can be identified as the PQ symmetry suitable for solving the strong CP problem within supersymmetric extensions of the Standard Model. In this case, U(1)${}_R$ is broken at some intermediate scale and the QCD axion is the R-axion. Moreover, the R-symmetry can be naturally gauged via the Green-Schwartz mechanism within completions to supergravity, thus evading the axion quality problem. Obstacles to realizing this scenario are highlighted and phenomenologically viable approaches are identified.