Representations of the Nappi--Witten vertex operator algebra

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.

arXiv comment21 pages; introduction expanded, references added, minor notation changes

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Cited by in corpus (3)

• Admissible-level ${\mathfrak{sl}}_3$ minimal models
• Non-relativistic quantum strings from gauged WZW models
• Representations of affine Nappi-Witten Lie algebras over polynomial algebras