Quantization and Algebraic Index
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909906191253504 |
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| author | Li, Si |
| author_facet | Li, Si |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12875 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantization and Algebraic Index Li, Si Mathematical Physics High Energy Physics - Theory Differential Geometry Quantum Algebra 81T40, 81T70, 81T75, 81S10 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. |
| title | Quantization and Algebraic Index |
| topic | Mathematical Physics High Energy Physics - Theory Differential Geometry Quantum Algebra 81T40, 81T70, 81T75, 81S10 |
| url | https://arxiv.org/abs/2511.12875 |