Discrete gauge theories
Abstract
In these lecture notes, we present a selfcontained discussion of planar gauge theories broken down to some finite residual gauge group H via the Higgs mechanism. The main focus is on the discrete H gauge theory describing the long distance physics of such a model. The spectrum features global H charges, magnetic vortices and dyonic combinations. Due to the AharonovBohm effect, these particles exhibit topological interactions. Among other things, we review the Hopf algebra related to this discrete H gauge theory, which provides an unified description of the spin, braid and fusion properties of the particles in this model. Exotic phenomena such as flux metamorphosis, Alice fluxes, Cheshire charge, (non)abelian braid statistics, the generalized spinstatistics connection and nonabelian AharonovBohm scattering are explained and illustrated by representative examples. Preface: Broken symmetry revisited, 1 Basics: 1.1 Introduction, 1.2 Braid groups, 1.3 Z_N gauge theory, 1.3.1 Coulomb screening, 1.3.2 Survival of the AharonovBohm effect, 1.3.3 Braid and fusion properties of the spectrum, 1.4 Nonabelian discrete gauge theories, 1.4.1 Classification of stable magnetic vortices, 1.4.2 Flux metamorphosis, 1.4.3 Including matter, 2 Algebraic structure: 2.1 Quantum double, 2.2 Truncated braid groups, 2.3 Fusion, spin, braid statistics and all that..., 3 \bar{D}_2 gauge theory: 3.1 Alice in physics, 3.2 Scattering doublet charges off Alice fluxes, 3.3 Nonabelian braid statistics, 3.A AharonovBohm scattering, 3.B B(3,4) and P(3,4), Concluding remarks and outlook
 Publication:

arXiv eprints
 Pub Date:
 November 1995
 arXiv:
 arXiv:hepth/9511201
 Bibcode:
 1995hep.th...11201D
 Keywords:

 High Energy Physics  Theory
 EPrint:
 85+2 pages, LaTeX, 13 eps figures uuencoded. Lectures presented by the second author at the CRMCAP Summer School `Particles and Fields 94', Bannf, Alberta, Canada, August 1624, 1994. Some minor typos corrected, references added, figures slightly changed, a discussion expanded. Postscript version also available at http://parthe.lpthe.jussieu.fr/~mdwp