PUZZLING COMBINATION - DISORDER X ORDER

There are several examples indicating that the operator combination disorder × order" creates anomalous spin and/or statistics. In 2 + 1 dimensions there is a similar anomaly related to the disorder operator carrying Z(N) topological charge believed to have an important role in quark confinement. The conventionally defined total angular momentum has an anomalous term 1 2σ3 (( 1 √3)λ8) and can take the values 1 2 ( 1 3) in the presence of "disorder × order" in 2 + 1 dimensional SU(2) (SU(#)) gauge theories. It is argued that the existence of a stable soliton solution or the introduction of Higgs fields are not important for the anomaly. © 1979."