Field Identification in Non-Unitary Diagonal Cosets

TL;DR

This paper investigates field identification in nonunitary diagonal cosets derived from admissible Kac-Moody algebra representations at fractional levels, using modular S matrix analysis to classify identifications.

Contribution

It provides a systematic analysis of field identifications, including nonunitary cases, and proposes a simple method for choosing coset field representatives.

Findings

Identifies classes of field identifications from the modular S matrix.

Includes nonunitary field identifications beyond outer automorphisms.

Proposes a straightforward way to select coset field representatives.

Abstract

We study the nonunitary diagonal cosets constructed from admissible representations of Kac-Moody algebras at fractional level, with an emphasis on the question of field identification. Generic classes of field identifications are obtained from the analysis of the modular S matrix. These include the usual class related to outer automorphisms, as well as some intrinsically nonunitary field identifications. They allow for a simple choice of coset field representatives where all field components of the coset are associated with integrable finite weights.