Derived gluing construction of chiral algebras

Abstract

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.

arXiv comment61 pages

References in corpus (16)

• Higher Topos Theory
• Vertex Algebras and Algebraic Curves
• Infinite Chiral Symmetry in Four Dimensions
• Vertex operator algebras, Higgs branches, and modular differential equations
• Chiral algebras of class S
• Shifted Poisson Structures and Deformation Quantization
• Lagrangian structures on mapping stacks and semi-classical TFTs
• Multiple Derived Lagrangian Intersections
• Abelianizing vertex algebras
• Derived coisotropic structures II: stacks and quantization
• Ring objects in the equivariant derived Satake category arising from Coulomb branches (with an appendix by Gus Lonergan)
• Chiral algebras of class $\mathcal{S}$ and Moore-Tachikawa symplectic varieties
• Representation Theory of W-Algebras
• Poisson reduction as a coisotropic intersection
• Arc spaces and chiral symplectic cores
• Lectures on shifted Poisson geometry

Cited by in corpus (1)

• Twisted chiral algebras of class $\mathcal{S}$ and mixed Feigin-Frenkel gluing