Chiral Homology of elliptic curves and the Zhu algebra
arXiv:1804.00017 · doi:10.1007/s00220-021-04026-w
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.
49 pages. Major expositional improvements requested by anonymous referee. To appear in CMP