Phase Structure of the Gauged Yukawa Model

Based on the ladder Schwinger-Dyson equation, we investigate phase struc-ture of the gauged Yukawa model possessing a global $SU(2)_L \times SU(2)_R$symmetry and an unbroken (vector-like) gauge symmetry. We show that even whenwe tune the squared mass of the scalar boson in the Lagrangian to be positive,there still exists the dynamical chiral symmetry breaking due to fermion paircondensate (VEV of the composite scalar) triggered by the strong Yukawacoupling larger than a certain critical value. We find a "nontrivialultraviolet fixed line" and "renormalized trajectories" in thethree-dimensional coupling space of the Yukawa coupling, the gauge cou- plingand the "hopping parameter" of the elementary scalar field. Presence of thegauge coupling is crucial to existence of the fixed line. Implications of theresult for the lattice calculation and the top quark condensate model are alsodiscussed.Comment: in LaTeX 44 pages +15 figures (figures are tared compressed uuencoded postscript file ;separated 3 parts), DPNU-93-45, CHIBA-EP-73, KEK-TH-380 and KEK Preprint 93-17