Abelian gauge structure and anomalous spin and statistics of solitons in non-linear sigma models

Abstract

We show that the inclusion of topological lagrangians in non-linear sigma models introduces certain topological non-trivial abelian background fields in the configuration space of these theories. In particular, the Hopf and the Wess-Zumino terms lead, respectively, to a vortex and a monopole in the corresponding configuration space for 2+1 and 3+1 dimensional theories. That topological solitons acquire anomalous spin and statistics through the inclusion of these lagrangians can be considered as the generalization of the situation for anyons and dyons in ordinary space to functional space.