论文标题
纳皮的表示形式 - witten顶点操作员代数
Representations of the Nappi--Witten vertex operator algebra
论文作者
论文摘要
NAPPI-WITTEN型号是一种Wess-Zumino-Witten模型，其中目标空间是非还原的Heisenberg Group $ H_4 $。我们考虑了这种保形场理论为基础的表示理论。具体来说，我们研究了与相关的仿射顶点操作员代数$ \ Mathsf {H} _4 $上的有限维重量空间的重量模块类别。特别是，我们对此类别中的不可约$ \ Mathsf {h} _4 $ -Modules进行分类并计算其字符。此外，我们观察到该类别是非膜膜的，这表明纳皮模型是对数的保形场理论。
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.
