Chiral Homology of elliptic curves and the Zhu algebra

Abstract

We study the chiral homology of elliptic curves with coefficients in a quasiconformal vertex algebra. Our main result expresses the nodal curve limit of the first chiral homology group in terms of the Hochschild homology of the Zhu algebra of V. A technical result of independent interest regarding the equivalence between the associated graded with respect to Li's filtration and the arc space of the C_2 algebra is presented.

arXiv comment49 pages. Major expositional improvements requested by anonymous referee. To appear in CMP

References in corpus (9)

• Vertex Algebras and Algebraic Curves
• Quantum Reduction for Affine Superalgebras
• Finite vs. affine W-algebras
• Rationality, quasirationality and finite W-algebras
• Abelianizing vertex algebras
• The variational Poisson cohomology
• Betti numbers of configuration spaces of surfaces
• Singular support of a vertex algebra and the arc space of its associated scheme
• A short construction of the Zhu algebra

Cited by in corpus (3)

• Boundary vertex algebras for 3d $\mathcal{N}=4$ rank-0 SCFTs
• Cosets of free field algebras via arc spaces
• Quasi-lisse vertex (super)algebras