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 univ erse. The fluctuations are created by numerical lattice simulations. I t is shown that a change in Chem-Simons number by one unit is accompan ied by eigenvalues crossing zero and a change of sip of the generalize d chirality GAMMA5 = (-1)2T+1gamma5 which labels these modes. This pro vides further evidence that the sphaleron-like configurations observed in lattice simulations may be viewed as representing continuum config urations.