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Representations of the Nappi--Witten vertex operator algebra
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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.
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Non-relativistic quantum strings from gauged WZW models
A chiral null gauging of Nappi-Witten WZW models yields a closed string with a Gomis-Ooguri-like spectrum, but with different left- and right-moving sectors.
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