论文标题
手性代数的胶合构造
Derived gluing construction of chiral algebras
论文作者
论文摘要
我们讨论$ \ Mathcal {s} $手性代数的粘合结构。 Arakawa引入了非衍生环境中的胶合结构，以构建一个顶点代数的家族，其相关品种为零属摩尔-Tachikawa属属构造。受较高属案例的动机，我们引入了DG顶点代数版本$ \ MATHSF {MT} _ {\ Mathrm {ch}} $的摩尔 - tachikawa symbletectic品种的类别的类别，其中一种dg pertex algebra的构造给出了一个dg pertex algebra的库，并构成了库的构造。 BRST还原。我们还表明，将相关方案从$ \ mathsf {mt} _ {\ mathrm {ch}} $提供给类别$ \ Mathsf {mtsf {mt} $的过程。
We discuss the gluing construction of class $\mathcal{S}$ chiral algebras in derived setting. The gluing construction in non-derived setting was introduced by Arakawa to construct a family of vertex algebras of which the associated varieties give genus zero Moore-Tachikawa symplectic varieties. Motivated by the higher genus case, we introduce a dg vertex algebra version $\mathsf{MT}_{\mathrm{ch}}$ of the category of Moore-Tachikawa symplectic varieties, where a morphism is given by a dg vertex algebra equipped with action of the universal affine vertex algebra, and composition of morphisms is given by the BRST reduction. We also show that the procedure taking the associated scheme of gives a functor from $\mathsf{MT}_{\mathrm{ch}}$ to the category $\mathsf{MT}$ of derived Moore-Tachikawa varieties, which would imply compatibility of gluing constructions in both categories.
