TeV scale 5D $SU(3)_W$ unification and the fixed point anomaly cancellation with chiral split multiplets

TL;DR

This paper explores 5D $SU(3)_W$ gauge unification with orbifold compactification, addressing fixed point anomalies via Chern-Simons terms and chiral fermions, and discusses implications for proton stability, mass hierarchies, and neutrino masses.

Contribution

It demonstrates anomaly cancellation in 5D $SU(3)_W$ models through Chern-Simons terms and chiral fermions at fixed points, providing a framework for realistic unification models.

Findings

Anomalies are canceled by Chern-Simons terms in simple models.

Fixed point U(1)--graviton--graviton anomaly cancels without Chern-Simons.

Chiral fermions at fixed points can ensure anomaly freedom in the effective 4D theory.

Abstract

A possibility of 5D gauge unification of $SU(2)_L \times U(1)_Y$ in $SU(3)_W$ is examined. The orbifold compactification allows fixed points where $SU(2)_L\times U(1)_Y$ representations can be assigned. We present a few possibilities which give long proton lifetime, top-bottom mass hierarchy from geometry, and reasonable neutrino masses. In general, these {\it chiral models} can lead to fixed point anomalies. We can show easily, due to the simplicity of the model, that these anomalies are cancelled by the relevant Chern-Simons terms for all the models we consider. It is also shown that the fixed point U(1)--graviton--graviton anomaly cancels without the help from the Chern-Simons term. Hence, we conjecture that the fixed point anomalies can be cancelled if the effective 4D theory is made anomaly free by locating chiral fermions at the fixed points.