Two-point Functions in Affine Current Algebra and Conjugate Weights

TL;DR

This paper constructs two-point functions in affine current algebras for all representations, enabling direct determination of conjugate field weights, regardless of integrability.

Contribution

It provides a comprehensive method to compute two-point functions for any representation in affine current algebras, including non-integrable cases.

Findings

Two-point functions are explicitly constructed for all representations.

Conjugate field weights are directly read off from the two-point functions.

The method applies to both integrable and non-integrable representations.

Abstract

The two-point functions in affine current algebras based on simple Lie algebras are constructed for all representations, integrable or non-integrable. The weight of the conjugate field to a primary field of arbitrary weight is immediately read off.