Elliptic Trace Map on Chiral Algebras
Abstract
Trace map on deformation quantized algebra leads to the algebraic index theorem. In this paper, we investigate a two-dimensional chiral analogue of the algebraic index theorem via the theory of chiral algebras developed by Beilinson and Drinfeld. We construct a trace map on the elliptic chiral homology of the free beta gamma-bc system using the BV quantization framework. As an example, we compute the trace evaluated on the unit constant chiral chain and obtain the formal Witten genus in the Lie algebra cohomology. We also construct a family of elliptic trace maps on coset models.
Keywords
Cite
@article{arxiv.2112.14572,
title = {Elliptic Trace Map on Chiral Algebras},
author = {Zhengping Gui and Si Li},
journal= {arXiv preprint arXiv:2112.14572},
year = {2022}
}
Comments
66 pages, 6 figures. v2: main theorem (Theorem 1.1) is strengthened by proving that our trace map is furthermore a quasi-isomorphism, an error in our Remark 3.10 is corrected;v3: Section 2.3 rewritten and proofs are simplified by showing the canonical trace map on the unit chiral chain complex coincides with regularized integrals. Remark 3.7 added, typos corrected