
TL;DR
This paper explores the connection between BV quantization and algebraic index theory, extending classical results to 2d chiral CFT and linking Gromov-Witten invariants with elliptic chiral indices in mirror symmetry.
Contribution
It introduces a novel approach to relate BV quantization with algebraic index theorems and extends the theory to elliptic chiral CFT, connecting Gromov-Witten invariants with mirror symmetry.
Findings
Classical algebraic index theorem proved via BV quantization.
Extension to 2d chiral CFT with elliptic index analog.
Gromov-Witten invariants linked to elliptic chiral index in mirror symmetry.
Abstract
This article reviews the program on connecting Batalin-Vilkovisky (BV) quantization with index theories of algebraic type. We explain how the classical algebraic index theorem can be proved in terms of BV quantization of topological quantum mechanics. This is generalized to 2d chiral CFT in which we present an elliptic chiral analog of the algebraic index theory. As an application, we show how the generating function of all genus Gromov-Witten invariants on elliptic curves is mirror equivalent to an elliptic chiral index in the mirror BCOV theory.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Black Holes and Theoretical Physics
