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

Latex file, 29 pages + 13 figures

References in corpus (3)

• Topography of the hot sphaleron Transitions
• The Level Crossing Phenomenon with Yukawa Interactions
• On sphaleron deformations induced by Yukawa interactions

Cited by in corpus (11)

• A construction of lattice chiral gauge theories
• Electroweak Baryon Number Non-Conservation in the Early Universe and in High Energy Collisions
• The classical sphaleron transition rate exists and is equal to $1.1({\alpha }_{w}T{)}^4$
• Real-Time Dynamics with Fermions on a Lattice
• Improved Hamiltonian for Minkowski Yang-Mills Theory
• Improved determination of the classical sphaleron transition rate
• Topological Defects with Non-Symmetric Core
• Spectral flow of chiral fermions in nondissipative Yang-Mills gauge field backgrounds
• $Z_2$ as the Topological Origin of B+L Violation in the Hot Electroweak Theory
• Path integral quantization of scalar fluctuations above a kink
• Real--time dynamics of a hot Yang-Mills theory: a numerical analysis