A Z(2) CLASSIFICATION FOR 2D FERMION LEVEL-CROSSING

Electroweak vortices may contribute to unsuppressed baryon violating p rocesses in the hot early universe. We explore a possible origin of th is phenomenon for a general 2-dimensional embedded defect. We demonstr ate that the number of fermionic zero modes of the static 2-dimensiona l Dirac operator in the background of SU(2) static gauge-Higgs field c onfigurations is a topological invariant module four. Static configura tions which are everywhere odd under parity with even-parity pure gaug e behaviour at infinity admit 4n, n is an element of Z, zero modes of the Jackiw-Rebbi (JR) type. Odd-parity configurations with odd-parity pure gauge behaviour at infinity are topologically disconnected from t he vacuum and admit 4n + 2 fermionic zero energy solutions. The classi fication implies the collapse of half of the fermion zero modes upon e mbedding a 2-dimensional gauge-Higgs configuration (string) with odd-p arity purl gauge behaviour at infinity into the 3-dimensional Minkowsk i space. (C) 1997 Published by Elsevier Science B.V.