Level Crossing for Hot Sphalerons

We study the spectrum of the Dirac Hamiltonian in the presence of high temperature sphaleron-like fluctuations of the electroweak gauge and Higgs fields, relevant for the conditions prevailing in the early universe. The fluctuations are created by numerical lattice simulations. It is shown that a change in Chern-Simons number by one unit is accompanied by eigenvalues crossing zero and a change of sign of the generalized chirality Γ̃5 = (−1)γ5 which labels these modes. This provides further evidence that the sphaleron-like configurations observed in lattice simulations may be viewed as representing continuum configurations. The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark National Technical University of Athens, Department of Physics, GR 157 80, Athens, Greece. Department of Physics, University of Wales, Swansea, Singleton Park, Swansea SA2 8PP, U.K.