A Survey of Vortices in Gauge Theories

Abstract

The objects in my talk this evening are possibly the least extended among those discussed in the past few mornings. They are the vortices of gauge theories, the grand daddy of all subsequent extended objects of renormalizable relativistic field theories. While the idea of using vortex filaments as fundamental objects traces back to Thomson1, Dirac2 and Buneman3, it has only recently flowed into the main stream of particle theory. This happened with the key suggestion of Nielsen and Olesen4 as well as Tassie5 that the Abrikosov flux line solution6 of the static Higgs-Kibble (alias Landau-Ginzburg) model can be identified with the celebrated Nambu string of dual resonance model7. Ever since there has been much activity on the subject. A glance at the literature shows a clear leveling off of papers on this topic. So it seems timely for you to sit back and for me to attempt a survey of this field. In a one hour talk, my presentation can only aim at an overview (which is probably what most of you are up to near the end of an active day); I must be very brief. All details are to be filled in at your own pace and leisure. For that purpose and for the record I have accumulated an extensive but certainly incomplete reference list on vortices. I must remark at the outset that much of what I will be talking about is essentially familiar to people in solid or liquid state physics.