Sphalerons and Strings

Abstract

This work is based on a paper with Margaret James, to appear in Phys Rev D. In it we showed that the dipole moment of the sphaleron has its origin in two components: a ring of electric current circulating around the edge of the sphaleron; and also two regions of opposite magnetic charge above and below the ring. This magnetic charge has a partly topological explanation, arising from the fact that the sphaleron is axisymmetric and parity invariant. Here, I discuss the definition of the electromagnetic field and its sources in the Standard Model, comparing the one we use with the better-known one of 't Hooft. I also discuss the resemblance between the sphaleron and Nambu's ``dumb-bell'' -- a segment of $Z$-string which connects a monopole to an antimonopole.