Five dimensional $SU(5) \times U(1)_{\rm PQ}$ grand unification

Abstract

We propose a grand unified model in five dimensions that addresses the strong CP problem. In this framework, the boundary conditions that break the unified gauge group into the Standard Model gauge group simultaneously explain the mass splitting of the new matter content required for gauge coupling unification and the emergence of the QCD axion as the $U(1)_{\rm PQ}$ gauge field. The quality of the axion solution is inherently ensured by the gauge symmetry of the model. We further investigate the implications of this setup, including its predictions for the proton decay rate, the detectability of axion dark matter, and its cosmological impact. Notably, the model predicts a proton decay signal within the sensitivity of upcoming experiments, a result driven by the trade-off between the unification scale and the reheating temperature. In our scenario, the scales of grand unification and the axion decay constant are naturally unified.