The spin-charge-family theory offers understanding of the triangle anomalies cancellation in the standard model

Abstract

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[{\tau }^{Ai}$${\tau }^{Bj}$${\tau }^{Ck}]$ --- where ${\tau }^{Ai},{\tau }^{Bi}$ and ${\tau }^{Ck}$ 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".

arXiv commentThere are several papers in this arxiv, apearing sequentially, the author of which is N. Mankoč Borštnik. The previous one with the title "Spin-charge-family theory is offering next step in understanding elementary particles and fields and correspondingly universe, making several predictions" includes one section with the topic of the present paper. 26 pages

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• A trial to understand the supersymmetry relations through extension of the second quantized fermion and boson fields, either to strings or to odd dimensional spaces