Tumbling and technicolor theory

We study the nonperturbative effect of induced four-fermion interactions in tumbling gauge theories by investigating the effective action in the one-gauge-boson exchange approximation. It is shown that the four-fermion couplings cannot become large enough to alter the qualitative feature of the original most attractive channel nor to realize the large anomalous dimension dynamics preferred by the realistic technicolor theory. The result implies that the gauge bosons which get masses in the process of tumbling decouple even nonperturbatively from the low-energy dynamics. The nonperturbative decoupling of fermions is also discussed