Axial anomaly and the triality symmetry of octonion

Abstract

With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as the quaternion makes an octonion, and the gauge field can be treated as self-dual, we calculate the axial current and two vector currents triangle diagram of Bardeen, which yields the contribution of the axial anomaly. The octonion possesses the triality symmetry, and there are 5 symmetry operations $G_{ij}$ and $G_{ijk}$ ($ijk=123)$, in which mixing of spinors and vectors occur. $G_{23}$ does not mix vectors and spinors, but mismatch of the spinor and vector fields occurs. Hence, electro magnetic (EM) wave emitted from galaxies transformed by the five transformations would not be detected by EM detectors in our galaxy, and the source would be regarded as dark matter. The axial anomaly appears as a reflection of the symmetry of the matter field and not as a reflection of the symmetry of the pure vacuum, which is consistent with recent arguments on condensates and confinement.

22 pages 25 figures, References and comments added, To be published in Few-Body Syst.(Springer)

References in corpus (9)

• Quark flavour effects on gluon and ghost propagators
• Maximum Wavelength of Confined Quarks and Gluons and Properties of Quantum Chromodynamics
• Sterile Neutrinos in Light of Recent Cosmological and Oscillation Data: a Multi-Flavor Scheme Approach
• Circumscribing Late Dark Matter Decays Model Independently
• Diffuse MeV Gamma-rays and Galactic 511 keV Line from Decaying WIMP Dark Matter
• QCD: Restoration of Chiral Symmetry and Deconfinement for Large N_f
• Bulk and finite-temperature transitions in SU(3) gauge theories with many light fermions
• Axial anomaly in quantum electro- and chromodynamics and the structure of the vacuum in quantum chromodynamics
• Domain Wall Fermion Lattice Simulation in Quaternion Basis

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