Random walk approximation in a chiral Yukawa-model and global symmetries

The fermion propagator is investigated in a chiral Yukawa-model with explicit mirror fermions applying the random walk approximation to the hopping parameter expansion. It is shown that the global SU(2)L⊗SU(2)R symmetry breaking due to the mass splitting within fermion doublets does influence the critical behaviour of the fermion spectrum in the continuum limit. In particular, in the case of a mirror pair of split doublets, where SU(2)L⊕SU(2)R is broken to SU(2)L, no evidence is found for a dynamical spectrum doubling at infinitely strong bare Yukawa-couplings, in contrast to the case with degenerate doublets and SU(2)L⊗SU(2)R symmetry