Representations of the Nappi--Witten vertex operator algebra

TL;DR

This paper investigates the representation theory of the Nappi-Witten vertex operator algebra, classifying irreducible modules, computing their characters, and revealing its nonsemisimple, logarithmic conformal field theory nature.

Contribution

It provides a classification of irreducible modules and character computations for the Nappi-Witten VOA, highlighting its nonsemisimple, logarithmic structure.

Findings

Classification of irreducible modules

Characters of modules computed

Identification of nonsemisimple, logarithmic structure

Abstract

The Nappi-Witten model is a Wess-Zumino-Witten model in which the target space is the nonreductive Heisenberg group $H_4$. We consider the representation theory underlying this conformal field theory. Specifically, we study the category of weight modules, with finite-dimensional weight spaces, over the associated affine vertex operator algebra $\mathsf{H}_4$. In particular, we classify the irreducible $\mathsf{H}_4$-modules in this category and compute their characters. We moreover observe that this category is nonsemisimple, suggesting that the Nappi-Witten model is a logarithmic conformal field theory.