The Spin‐Charge‐Family Theory Offers Understanding of the Triangle Anomalies Cancellation in the Standard Model

• Published in: Fortschritte der Physik 2017-12, Vol.65 (12), p.n/a
• Main Authors: Mankoč Borštnik, N. S., Nielsen, H. B. F.
• Format: Article
• Language: English
• Subjects: 11.10.Kk; 11.30.‐j; 12.60.Cn; 12.60.Fr; 12.60.‐i; Anomalies; Anomaly cancellation; Beyond the standard model; Cancellation; Fermions; Generators; Handedness; Kaluza‐Klein‐like theoriesPACS numbers: 12.10.‐g; Leptons; Quarks; Representations; Subgroups; Unifying theories
• ISSN: 0015-8208; 1521-3978
• DOI: 10.1002/prop.201700046

The standard model has for massless quarks and leptons “miraculously” no triangle anomalies due to the fact that the sum of all possible traces Tr[τAiτBjτCk] — where τAi,τBi and τCk are the generators of one, of two or of three of the groups SU(3),SU(2) and U(1) — over the representations of one family of the left handed fermions and anti‐fermions (and separately of the right handed fermions and anti‐fermions), contributing to the triangle currents, is equal to zero. It is demonstrated in this paper that this cancellation of the standard model triangle anomaly follows straightforwardly if the SO(3,1),SU(2),U(1) and SU(3) are the subgroups of the orthogonal group SO(13,1), as it is in the spin‐charge‐family theory. We comment on the SO(10) anomaly cancellation, which works if handedness and charges are related “by hand”. The standard model has for massless quarks and leptons “miraculously” no triangle anomalies due to the fact that the sum of all possible traces T r[τAi τBj τCk] — where , τAi τBj and τCk are the generators of one, of two or of three of the groups SU(3), SU(2) and U(1) — over the representations of one family of the left handed fermions and anti‐fermions (and separately of the right handed fermions and anti‐fermions), contributing to the triangle currents, is equal to zero. It is demonstrated in this paper that this cancellation of the standard model triangle anomaly follows straightforwardly if the SO(3, 1), SU(2), U(1) and SU(3) are the subgroups of the orthogonal group SO(13,1), as it is in the spin‐charge‐family theory. The authors comment on the SO(10) anomaly cancellation, which works if handedness and charges are related “by hand”.