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

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.