Topological content of the electroweak sphaleron on the lattice

• Published in: Physics letters. B Vol. 424; no. 1; pp. 106 - 114
• Main Authors: Chernodub, M.N, Gubarev, F.V, Ilgenfritz, E.-M
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 02.04.1998
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/S0370-2693(98)00101-4

3 D electroweak sphalerons on the lattice are used as test configurations for definitions of various topological defects. In the maximally Abelian gauge they are shown to contain a symmetric array of Abelian monopoles and anti-monopoles connected by two kinds of Abelian vortex strings. Gauge-invariant lattice definitions of the Nambu monopole and the Z-vortex string are formulated which correspond to Abelian projection from the unitary gauge. The sphalerons contain in their core just one (non-Abelian) Nambu monopole–anti-monopole pair (connected by a Z-string) in an unstable saddle point bound state. This provides an example for the monopole-pair unbinding mechanism expected to work at the electroweak phase transition. The definitions of defects developed here will be used in future studies of topological aspects of this transition.