Semi-Classical Blocks and Correlators in Rational and Irrational Conformal Field Theory

TL;DR

This paper develops a unified approach to conformal blocks and correlators in both rational and irrational conformal field theories using generalized Knizhnik-Zamolodchikov equations, extending known solutions to new classes.

Contribution

It introduces a method to construct high-level conformal blocks and correlators for a broad class of irrational conformal field theories, building on solutions from rational cases.

Findings

Constructed conformal blocks for affine-Sugawara and coset models.

Identified a simple class of irrational processes with explicit correlators.

Unified description of rational and irrational conformal field theories.

Abstract

The generalized Knizhnik-Zamolodchikov equations of irrational conformal field theory provide a uniform description of rational and irrational conformal field theory. Starting from the known high-level solution of these equations, we first construct the high-level conformal blocks and correlators of all the affine-Sugawara and coset constructions on simple g. Using intuition gained from these cases, we then identify a simple class of irrational processes whose high-level blocks and correlators we are also able to construct.