ON SPHALERON DEFORMATIONS INDUCED BY YUKAWA INTERACTIONS

Due to the presence of the chiral anomaly sphalerons, half a number of Chern-Simons (CS = 1/2) are the only static configurations that allow a fermion level crossing in the two-dimensional Abelian-Higgs model w ith massless fermions, i.e. in the absence of Yukawa interactions. In the presence of fermion-Higgs interactions we demonstrate the existenc e of zero energy solutions to the one-dimensional Dirac equation at de formed sphalerons with CS not-equal 1/2. Induced level crossing due to Yukawa interactions illustrates a non-trivial generalization of the A tiyah-Patodi-Singer index theorem and of the equivalence between parit y anomaly in odd and chiral anomaly in even dimensions. We discuss a s ubtle manifestation of this effect in the standard electroweak theory at finite temperatures.