A superstructure over the Farhi - Susskind Technicolor model

TL;DR

This paper proposes an extended gauge group superstructure over the Farhi-Susskind Technicolor model, incorporating an infinite sequence of SU(N) groups and a discrete symmetry, aiming to maintain anomaly cancellation and symmetry preservation.

Contribution

It introduces a novel superstructure of gauge groups extending the Farhi-Susskind model, ensuring anomaly freedom and discrete symmetry preservation through specific hypercharge assignments.

Findings

Existence of hypercharge assignments that cancel anomalies.

Preservation of the discrete symmetry $ ext{ extcal Z}$ in the extended model.

Construction of a consistent superstructure over the original model.

Abstract

We suggest the model with the gauge group $ ... \otimes SU(6) \otimes SU(5)\otimes SU(4) \otimes SU(3) \otimes SU(2) \otimes U(1)$. This group is the infinite continuation of the gauge group $SU(4) \otimes SU(3) \otimes SU(2) \otimes U(1)$ of Farhi - Susskind model. The constructed model contains fermions from the fundamental representations of any SU(N) subgroups of the gauge group. In the construction of the model we use essentially the requirement that it posseses an additional discrete symmetry $\cal Z$ that is the continuation of the $Z_6$ symmetry of the Standard Model. It has been found that there exists such a choice of the hypercharges of the fermions that the chiral anomaly is absent while the symmetry $\cal Z$ is preserved.