论文标题
Bershadsky-Polyakov顶点代数为正整数和二元性
Bershadsky-Polyakov vertex algebras at positive integer levels and duality
论文作者
论文摘要
我们研究简单的Bershadsky-Polyakov代数$ \ MATHCAL W_K = \ MATHCAL {W} _K（Sl_3，f_θ）$在正整数级别上并分类其不可约解的模块。通过这种方式，我们确认了Arxiv：1910.13781的猜想。接下来，我们研究案例$ k = 1 $。我们发现，这个顶点代数具有Kazama-suzuki型双重异构，用于简单的Afine顶点superalgebra $ l_ {k'}（osp（1 \ vert 2））$ for $ k'= -5/4 $。使用$ l_ {k'}（osp（1 \ vert 2））$的自由场实现：1711.11342，我们可以自由地实现$ \ Mathcal W_k $及其最高权重模块。在续集中，我们计划研究$ \ Mathcal W_K $的融合规则。
We study the simple Bershadsky-Polyakov algebra $\mathcal W_k = \mathcal{W}_k(sl_3,f_θ)$ at positive integer levels and classify their irreducible modules. In this way we confirm the conjecture from arXiv:1910.13781. Next, we study the case $k=1$. We discover that this vertex algebra has a Kazama-Suzuki-type dual isomorphic to the simple afine vertex superalgebra $L_{k'} (osp(1 \vert 2))$ for $k'=-5/4$. Using the free-field realization of $L_{k'} (osp(1 \vert 2))$ from arXiv:1711.11342, we get a free-field realization of $\mathcal W_k$ and their highest weight modules. In a sequel, we plan to study fusion rules for $\mathcal W_k$.
