Z(2) AS THE TOPOLOGICAL ORIGIN OF B+L VIOLATION IN THE HOT ELECTROWEAK THEORY

The space of static finite-energy configurations in the electroweak th eory admits a Z(2) 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 classific ation extends the description of baryon- and lepton-number violating e lectroweak processes to the symmetric phase of the theory. Configurati ons with odd pure-gauge behaviour at spatial infinity, such as the sph aleron, multisphalerons, as well as an infinite surface of their equiv alents, have half-integer Chem-Simons number and mediate B + L violati ng processes in the early universe. Finite-energy configurations with even pure-gauge behaviour, such as the S new sphaleron, are topologic ally equivalent to the vacuum and are irrelevant for B + L violation. Electroweak string configurations comprise continuous families of spha leron equivalents as well as configurations equivalent to the vacuum. We discuss the possible formation of B + L violating quark-lepton cond ensates in the symmetric high-temperature phase of the electroweak the ory.