Level Crossing for Hot Sphalerons

Abstract

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 $\text{tGf}=(-1{)}^{2T+1}\text{gf}$ which labels these modes. This provides further evidence that the sphaleron-like configurations observed in lattice simulations may be viewed as representing continuum configurations.

Comments: Latex file, 29 pages + 13 figures