A non-Abelian square root of Abelian vertex operators

Abstract

The quantum field theoretical formulation of Kadanoff’s “correlations along a line” in the critical two-dimensional Ising model is given in terms of p-products of Wightman fields. It provides a quadratic factorization, in the sense of operator-valued distributions, of Abelian chiral vertex operators into non-Abelian exchange fields. This basic result implies p-polynomial relations between fields from various conformal models in two dimensions; notably the two-dimensional local fields with chiral SU(2) symmetry at level 2 are shown to share the nontrivial peculiarities of the Ising model order and disorder fields. These examples have interesting implications for the properties of p-products in general.