Top mode standard model with extra dimensions

We critically examine a version of the top mode standard model recently cast in extra dimensions by Arkani-Hamed, Cheng, Dobrescu, and Hall, based on the (improved) ladder Schwinger-Dyson (SD) equation for the D- (= 6,8-) dimensional gauge theories. We find that the bulk QCD cannot have larger coupling beyond the nontrivial 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 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 find that the improved ladder SD equation in D dimensions has an approximate scale invariance due to the running of the coupling and hence has an essential-singularity scaling of the "conformal phase transition," similar to Miransky scaling in the four-dimensional ladder SD equation with a nonrunning coupling. This essential-singularity scaling can resolve the fine-tuning even when the cutoff ("string scale") is large. Such a theory has a large anomalous dimension gamma (m) = D/2 - 1 and is expected to be free from the flavor-changing-neutral-current problem as in walking technicolor for D = 4. Furthermore, the induced bulk Yukawa coupling becomes finite even at infinite cutoff limit (in the formal sense), similar to the renormalizability of the gauged Nambu-Jona-Lasinio model. Comments are made on the use of the "effective" coupling, which includes finite renormalization effects, instead of the (MS) over bar running coupling in the improved ladder SD equation.