On Principal Admissible Representations and Conformal Field Theory

TL;DR

This paper investigates principal admissible representations of affine Kac-Moody algebras and their application to conformal field theory, focusing on generating highest weights and null vectors for $A_r^{(1)}$ at rational levels.

Contribution

It introduces a new algorithm for generating null vectors and clarifies the role of field identifications in describing primary fields in nonunitary coset theories.

Findings

Generated principal admissible highest weights for $A_r^{(1)}$

Developed an algorithm for null vector production

Proved the impact of field identifications on primary field descriptions

Abstract

The principal admissible representations of affine Kac-Moody algebras are studied, with a view to their use in conformal field theory. We discuss the generation of the set of principal admissible highest weights, concentrating mainly on $A_r^{(1)}$ at rational level $k$. A related algorithm is described that produces the Malikov-Feigen-Fuchs null vectors of these representations. With the principal admissible description of the highest weights, we are able to prove that field identifications (including maverick ones) lead to the canonical description of the primary fields of the nonunitary diagonal coset theories.