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Elliptic Trace Map on Chiral Algebras

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arxiv 2112.14572 v3 pith:HHDNYAW5 submitted 2021-12-29 math.QA hep-thmath-phmath.AGmath.MP

Zhengping Gui , Si Li This is my paper · ORCID
classification math.QAhep-thmath-phmath.AGmath.MP
keywords chiraltraceellipticalgebraalgebraicalgebrasconstructindex
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Higher Chiral Algebras in a Polysimplicial Model

    math.QA 2025-06 conditional novelty 8.0 of 10

    The polysimplicial model makes the shifted canonical sheaf on A^n into a homotopy chiral algebra, with the Lie-infinity operad quasi-isomorphic to the operad of chiral operations.

  2. Higher-dimensional Chiral Algebras in the Jouanolou Model and free-field realization

    math.QA 2025-10 conditional novelty 7.0 of 10

    The authors define d-dimensional homotopy chiral algebras in a Jouanolou model, construct the unit such algebra from Feynman-graph residues, and realize higher Kac-Moody and Virasoro structures via free fields.

  3. Contact Term Algebras and Dijkgraaf's Master Equation

    math.QA 2025-06 accept novelty 6.0 of 10

    A rigorous derivation of Dijkgraaf's master equation for chiral torus deformations, built from a vertex algebra contact term algebra and modified A-cycle integrals.

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