Parafermionic excitations and critical exponents of random cluster and O(n) models

TL;DR

This paper introduces parafermionic fields in two-dimensional conformal field theory to derive critical exponents for random cluster and O(n) models, linking scattering theory with conformal dimensions and providing new insights for non-rational theories.

Contribution

It presents a novel approach using scale invariant scattering theory to determine parafermionic conformal dimensions and derive critical exponents for complex models.

Findings

Derived critical exponents for random cluster and O(n) models.

Linked S-matrix and Lagrangian couplings in sine-Gordon model.

Provided new methods for non-rational conformal theories.

Abstract

We introduce the notion of parafermionic fields as the chiral fields which describe particle excitations in two-dimensional conformal field theory, and argue that the parafermionic conformal dimensions can be determined using scale invariant scattering theory. Together with operator product arguments this may provide new information, in particular for non-rational conformal theories. We obtain in this way the field theoretical derivation of the critical exponents of the random cluster and O(n) models, which in the limit of vanishing central charge yield percolation and self-avoiding walks. A simple derivation of the relation between S-matrix and Lagrangian couplings of sine-Gordon model is also given.