Bergman space, Conformally flat 2-disk operads and affine Heisenberg vertex algebra
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910043868233728 |
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| author | Moriwaki, Yuto |
| author_facet | Moriwaki, Yuto |
| contents | In this paper we consider the operad of holomorphic disk embeddings of the unit disk $\mathbb D \subset \mathbb C$. We introduce a suboperad $\mathbb{CE}_2^{HS}$ defined by square-integrability conditions and show that the symmetric algebra $\mathrm{Sym} A^{2}(\mathbb D)$ of the Bergman space carries a natural $\mathbb{CE}_2^{HS}$-algebra structure. Conformally flat factorization homology with coefficients in $\mathrm{Sym} A^{2}(\mathbb D)$ then yields metric-dependent invariants of two-dimensional Riemannian manifolds. Moreover, $\mathrm{Sym} A^{2}(\mathbb D)$ is identified with the ind-Hilbert space completion of the affine Heisenberg vertex operator algebra. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_06491 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bergman space, Conformally flat 2-disk operads and affine Heisenberg vertex algebra Moriwaki, Yuto Quantum Algebra Mathematical Physics Differential Geometry In this paper we consider the operad of holomorphic disk embeddings of the unit disk $\mathbb D \subset \mathbb C$. We introduce a suboperad $\mathbb{CE}_2^{HS}$ defined by square-integrability conditions and show that the symmetric algebra $\mathrm{Sym} A^{2}(\mathbb D)$ of the Bergman space carries a natural $\mathbb{CE}_2^{HS}$-algebra structure. Conformally flat factorization homology with coefficients in $\mathrm{Sym} A^{2}(\mathbb D)$ then yields metric-dependent invariants of two-dimensional Riemannian manifolds. Moreover, $\mathrm{Sym} A^{2}(\mathbb D)$ is identified with the ind-Hilbert space completion of the affine Heisenberg vertex operator algebra. |
| title | Bergman space, Conformally flat 2-disk operads and affine Heisenberg vertex algebra |
| topic | Quantum Algebra Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2603.06491 |