论文标题
gaiotto-rapčák$ y $ - 代数的Orbifolds
Orbifolds of Gaiotto-Rapčák $Y$-algebras
论文作者
论文摘要
通用的两参数$ {\ MATHCAL W} _ {\ infty} $ - 代数是类型$ {\ Mathcal W}的顶点代数的分类对象（\ Mathcal W}（2,3，\ dots，dots，n）$。 Gaiotto和Rapčák最近推出了一个称为$ y $ y-Algebras的大型偏顶代数，其中包括许多已知的示例，例如主要$ {\ Mathcal W} $ - 类型$ a $的代数。这些代数承认$ \ mathbb {z} _2 $的动作，在本文中，我们研究了它们的Orbifolds的结构。除了Virasoro代数或$ {\ Mathcal W} _3 $ -Algebra的极端情况外，我们还表明，这些Orbifolds是由单个字段中的保量重量$ 4 $生成的，我们给出了强有限的有限生成集。
The universal two-parameter ${\mathcal W}_{\infty}$-algebra is a classifying object for vertex algebras of type ${\mathcal W}(2,3,\dots, N)$ for some $N$. Gaiotto and Rapčák recently introduced a large family of such vertex algebras called $Y$-algebras, which includes many known examples such as the principal ${\mathcal W}$-algebras of type $A$. These algebras admit an action of $\mathbb{Z}_2$, and in this paper we study the structure of their orbifolds. Aside from the extremal cases of either the Virasoro algebra or the ${\mathcal W}_3$-algebra, we show that these orbifolds are generated by a single field in conformal weight $4$, and we give strong finite generating sets.
