Categorical Enumerative Invariants, II: Givental formula
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866913728828538880 |
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| author | Caldararu, Andrei Tu, Junwu |
| author_facet | Caldararu, Andrei Tu, Junwu |
| contents | To a pair $(A,s)$ consisting of a smooth, cyclic $A_\infty$-algebra $A$ and a splitting $s$ of the Hodge filtration on its Hochschild homology Costello (2005) associates an invariant which conjecturally generalizes the total descendant Gromov-Witten potential of a symplectic manifold.
In this paper we give explicit, computable formulas for Costello's invariants, as Feynman sums over partially directed stable graphs. The formulas use in a crucial way the combinatorial string vertices defined earlier by Costello and the authors. Explicit computations elsewhere confirm in many cases the equality of categorical invariants with known Gromov-Witten, Fan-Jarvis-Ruan-Witten, and Bershadsky-Cecotti-Ooguri-Vafa invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_06659 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Categorical Enumerative Invariants, II: Givental formula Caldararu, Andrei Tu, Junwu Symplectic Geometry Algebraic Geometry 53D45, 14N35, 57K20 To a pair $(A,s)$ consisting of a smooth, cyclic $A_\infty$-algebra $A$ and a splitting $s$ of the Hodge filtration on its Hochschild homology Costello (2005) associates an invariant which conjecturally generalizes the total descendant Gromov-Witten potential of a symplectic manifold. In this paper we give explicit, computable formulas for Costello's invariants, as Feynman sums over partially directed stable graphs. The formulas use in a crucial way the combinatorial string vertices defined earlier by Costello and the authors. Explicit computations elsewhere confirm in many cases the equality of categorical invariants with known Gromov-Witten, Fan-Jarvis-Ruan-Witten, and Bershadsky-Cecotti-Ooguri-Vafa invariants. |
| title | Categorical Enumerative Invariants, II: Givental formula |
| topic | Symplectic Geometry Algebraic Geometry 53D45, 14N35, 57K20 |
| url | https://arxiv.org/abs/2009.06659 |