B+L Violation in the Hot Electroweak Theory

The space of static finite-energy configurations in the electroweak theory admits a Z2 topological structure. More precisely, we show that this space contains two disconnected sectors of unstable gauge-Higgs fields odd under a properly defined generalized parity. This classification extends the description of baryon and lepton number violating electroweak processes to the symmetric phase of the theory. Configurations with odd pure-gauge behaviour at spatial infinity, such as the sphaleron, multisphalerons, electroweak strings as well as an infinite surface of their equivalents, have half-integer Chern-Simons number and mediate B + L violating processes in the early universe. Finite-energy configurations with even pure-gauge behaviour, such as the S new sphaleron and electroweak strings, are topologically equivalent to the vacuum and are irrelevant for B + L violation. We discuss the possible formation of B + L violating quark-lepton condensates in the symmetric high-temperature phase of the electroweak theory. e-mail: [email protected] e-mail: [email protected], [email protected] e-mail: [email protected] Present address: NASA/Fermilab Astrophysics Center, MS-209, P.O. Box 500, Batavia, IL 60510, USA; e-mail: [email protected]