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arXiv · 2011.14453

Representations of the Nappi--Witten vertex operator algebra

Andrei Babichenko·Kazuya Kawasetsu·David Ridout·William Stewart
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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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Andrei Babichenko, Kazuya Kawasetsu, David Ridout, William Stewart. 2021-10-01. Representations of the Nappi--Witten vertex operator algebra. https://doi.org/10.1007/s11005-021-01471-5

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