Dark matter as ultralight axion-like particle in E6 x U(1)X GUT with QCD axion

Axion-like fields are naturally generated by a mechanism of anomaly cancellation of one or more anomalous gauge abelian symmetries at the Planck scale, emerging as duals of a two-form from the massless bosonic sector of string theory. This suggests an analogy of the Green-Schwarz mechanism of anomaly cancellation, at field theory level, which results in one or more Stueckelberg pseudoscalars. In the case of a single Stueckelberg pseudoscalarb, vacuum misalignments at phase transitions in the early Universe at the GUT scale provide a small mass-due to instanton suppression of the periodic potentialfor a component of b, denoted as chi and termed the axi-Higgs, which is a physical axion-like particle. The coupling of the axi-Higgs to the gauge sector via Wess-Zumino terms is suppressed by the Planck mass, which guarantees its decoupling, while its angle of misalignment is related to M-GUT. We build a gauged E-6 x U(1) model with anomalous U(1). It contains both an automatic invisible QCD axion and an ultra-light axi-Higgs. The invisible axion present in the model solves the strong CP problem and has mass in the conventional range while the axi-Higgs, which can act as dark matter, is sufficiently light (10(-22) eV < m(chi) < 10(-20) eV) to solve short-distance problems which confront other cold dark matter candidates. (C) 2018 The Author(s). Published by Elsevier B.V.