关于源自秩一4D SCFT的非容许水平上的若干简单轨形仿射VOA
On some simple orbifold affine VOAs at non-admissible level arising from rank one 4D SCFTs
AI总结：
本文研究源自秩一4D SCFT的非容许水平仿射顶点代数，分类$L_{-2}(G_2)$与$L_{-2}(B_3)$的不可约最高权模，并证明前者的伴生簇是$L_{-2}(D_4)$伴生簇在三次对称群下的轨形。
摘要：
我们研究了源自秩一4D SCFT的、处于非容许水平的若干简单仿射顶点代数的表示。具体而言，我们分类了$L_{-2}(G_2)$与$L_{-2}(B_3)$的不可约最高权模。由Adamović和Perše的工作已知，这些顶点代数可以共形嵌入到$L_{-2}(D_4)$中。我们还计算了$L_{-2}(G_2)$的伴生簇，并证明它是$L_{-2}(D_4)$的伴生簇在三次对称群作用下的轨形，该群正是$D_4$的Dynkin图自同构群。这提供了一个有趣的新伴生簇例子，满足轨形顶点代数背景下的若干猜想。
英文摘要：
We study the representations of some simple affine vertex algebras at non-admissible level arising from rank one 4D SCFTs. In particular, we classify the irreducible highest weight modules of $L_{-2}(G_2)$ and $L_{-2}(B_3)$. It is known by the works of Adamović and Perše that these vertex algebras can be conformally embedded into $L_{-2}(D_4)$. We also compute the associated variety of $L_{-2}(G_2)$, and show that it is the orbifold of the associated variety of $L_{-2}(D_4)$ by the symmetric group of degree 3 which is the Dynkin diagram automorphism group of $D_4$. This provides a new interesting example of associated variety satisfying a number of conjectures in the context of orbifold vertex algebras.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
