Chiral correlators of the Ising conformal field theory

TL;DR

This paper derives explicit conformal blocks for the Ising conformal field theory, revealing identities between bosonic and fermionic descriptions and extending results to the su(2)_2 WZW model.

Contribution

It provides explicit formulas for Ising conformal blocks from bosonization and uncovers identities linking different descriptions, advancing theoretical understanding.

Findings

Explicit conformal blocks for arbitrary primary fields derived

Identities between bosonic and fermionic correlators established

Extensions to su(2)_2 WZW conformal blocks obtained

Abstract

We derive explicit expressions for the conformal blocks of the Ising conformal field theory, for the correlators of an arbitrary number of primary fields. These results are obtained from the bosonized description of the Ising model. Interestingly, correlators involving Majorana fermions, can be obtained in two different ways, giving rise to identities between the `bosonic' and `fermionic' description of these correlators. These identities are generalizations of the famous Cauchy-identity. The conformal blocks of the Ising model are used to derive expression for the conformal blocks of the su(2)_2 WZW conformal field theory.