Top Mode Standard Model with Extra Dimensions

We critically examined a version of the top mode standard model recently cast in the extra dimensions by Arkani-Hamed et al., based on the (improved) ladder Schwinger-Dyson (SD) equation for the D(= 6,8)-dimensional gauge theories. We found that the bulk QCD cannot have larger coupling beyond the non-trivial ultraviolet (UV) fixed point, the existence of which is supported by a recent lattice analysis. The coupling strength at the fixed point is evaluated by using the one-loop renormalization group equation. It is then found that, in a version with only the third family (as well as the gauge bosons) living in the D-dimensional bulk, the critical (dimensionless) coupling for the dynamical chiral symmetry breaking to occur is larger than the UV fixed point of the bulk QCD coupling for D = 6, while smaller for D = 8. We further found that the improved ladder SD equation in D dimensions has an approximate scale-invariance due to running of the coupling and hence has an essential-singularity scaling of the “conformal