Topological Content of the Electroweak Sphaleron on the Lattice

Abstract

3D 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.