Non-Abelian solitons in two-dimensional lattice field theories

Abstract

For a class of self-interacting multicomponent scalar field theories with a global discrete non-Abelian symmetry group, mixed order–disorder correlation functions are defined in terms of Euclidean functional integrals. These correlation functions satisfy Osterwalder–Schrader positivity. From a representation of the correlation functions in terms of the transfer matrix, the dual algebra at fixed time is derived. This algebra implies parafermion operators showing non-Abelian braid group statistics. In a pure phase of spontaneous symmetry breaking for a related class of order–disorder correlation functions a convergent polymer representation is developed, emerging from a combined low- and high-temperature-type expansion. The infinite volume correlation functions of this class show exponential clustering in the disorder fields.