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

TL;DR

This paper explains the anomaly cancellation in the Standard Model through the spin-charge-family theory, showing it naturally arises from the embedding of Standard Model groups into the larger orthogonal group SO(13,1).

Contribution

It demonstrates that the Standard Model's triangle anomaly cancellation is a direct consequence of the spin-charge-family theory's group structure, specifically the embedding into SO(13,1).

Findings

Anomaly cancellation follows from SO(13,1) subgroup structure.

Standard Model groups are subgroups of SO(13,1).

Comments on SO(10) anomaly cancellation are included.

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".