A nonabelian square root of abelian vertex operators

Details A nonabelian square root of abelian vertex operators A nonabelian square root of abelian vertex operators

1997-05-06

arxiv.org/abs/hep-th/9705033v2

J.Math.Phys.39:3073-3090,1998

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, AMS-TeX, minor improvements

Scientific paper

10.1063/1.532240

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.

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