Chiral Homology of elliptic curves and the Zhu algebra
Jethro van Ekeren, Reimundo Heluani
TL;DR
This paper investigates the chiral homology of elliptic curves in the context of vertex algebras, revealing a connection to Hochschild homology of the Zhu algebra and exploring related algebraic structures.
Contribution
It establishes a link between the chiral homology of elliptic curves and Hochschild homology of the Zhu algebra, including a new technical result on algebraic filtrations.
Findings
The nodal curve limit of the first chiral homology is expressed via Hochschild homology.
A new equivalence between associated graded structures and arc spaces is demonstrated.
The study provides insights into the algebraic structures underlying vertex algebras.
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.
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