A nonabelian square root of abelian vertex operators

TL;DR

This paper explores a novel non-abelian square root construction of abelian vertex operators, revealing new insights into conformal coset models and the relation between the Ising model and free massless Dirac theory.

Contribution

It introduces a non-abelian framework for abelian vertex operators, providing new explanations for their relations to other models and symmetries.

Findings

Reveals a non-abelian square root of abelian vertex operators.

Establishes properties of local fields with chiral SU(2) symmetry.

Connects the Ising model with free massless Dirac theory.

Abstract

Kadanoff's "correlations along a line" in the critical two-dimensional Ising model (1969) 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. 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 established for the two-dimensional local fields with chiral level 2 SU(2) symmetry.