# A nonabelian square root of abelian vertex operators

Source: [A nonabelian square root of abelian vertex operators](<https://www.sota2.com/research/paper/68fa23252c2a3760193932c3>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T05:59:47.306Z

Authors: K. Frieler, K.-H. Rehren

Published: 1997-05-06T11:20:53.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/hep-th/9705033>)

[PDF](<https://arxiv.org/pdf/hep-th/9705033.pdf>)