Fermionic Coset Realization of Primaries in Critical Statistical Models

TL;DR

This paper presents a fermionic coset approach to realize primaries in minimal models, demonstrating explicit constructions for the Ising model and confirming four-point functions match known results.

Contribution

It introduces a fermionic coset framework for minimal models and explicitly constructs key operators in the Ising model, linking algebraic and correlator computations.

Findings

Explicit realization of energy, order, and disorder operators in the Ising model.

Four-point functions computed match existing results.

Provides a new fermionic approach to minimal models.

Abstract

We obtain a fermionic coset realization of the primaries of minimal unitary models and show how their four-point functions may be calculated by the use of a reduction formula. We illustrate the construction for the Ising model, where we obtain an explicit realization of the energy operator, Onsager fermions, as well as of the order and disorder operators realizing the dual algebra, in terms of constrained Dirac fermions. The four-point correlators of these operators are shown to agree with those obtained by other methods.