A non-abelian square root of abelian vertex operators

Kadanoff’s “correlations along a line” in the critical two-dimensional Ising model [1] are reconsidered. They are the analytical aspect of a representation of abelian chiral vertex operators as quadratic polynomials, in the sense of operator valued distributions, in non-abelian exchange fields. This basic result has interesting applications to conformal coset models. It also gives a new explanation for the remarkable relation between the “doubled” critical Ising model and the free massless Dirac theory [2]. As a consequence, analogous properties as for the Ising model order/disorder fields with respect both to doubling and to restriction along a line are found for the two-dimensional local fields with chiral SU(2) symmetry at level 2. PACS classification: 03.70, 11.10.L, 11.25.H