Prefactorization algebras for the conformal Laplacian: Central charge and Hilbert Fock space
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2026
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| _version_ | 1866914468811767808 |
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| author | Moriwaki, Yuto |
| author_facet | Moriwaki, Yuto |
| contents | Let $d \geq 2$. We consider the symmetric monoidal category of oriented Riemannian $d$-manifolds with conformal open embeddings. The prefactorization algebra associated with the conformal Laplacian defines a symmetric monoidal functor from this category to real vector spaces. For Euclidean domains $U\subset\mathbb{R}^d$, the value of this functor is identified, via the Green function, with the symmetric algebra on the topological dual of the space of harmonic functions. For $d \geq 3$ this identification is natural under all conformal transformations, while in dimension two, its failure of naturality is governed by a harmonic cocycle, which plays the role of a central charge. For the unit disk, the resulting vector space carries an algebra structure over the operad of conformal disk embeddings and admits a canonical dense embedding into the Hilbert Fock space. In dimension two, this statement holds after restricting to a codimension-one subspace, as suggested by logarithmic CFT. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_17549 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Prefactorization algebras for the conformal Laplacian: Central charge and Hilbert Fock space Moriwaki, Yuto Mathematical Physics Differential Geometry Quantum Algebra Let $d \geq 2$. We consider the symmetric monoidal category of oriented Riemannian $d$-manifolds with conformal open embeddings. The prefactorization algebra associated with the conformal Laplacian defines a symmetric monoidal functor from this category to real vector spaces. For Euclidean domains $U\subset\mathbb{R}^d$, the value of this functor is identified, via the Green function, with the symmetric algebra on the topological dual of the space of harmonic functions. For $d \geq 3$ this identification is natural under all conformal transformations, while in dimension two, its failure of naturality is governed by a harmonic cocycle, which plays the role of a central charge. For the unit disk, the resulting vector space carries an algebra structure over the operad of conformal disk embeddings and admits a canonical dense embedding into the Hilbert Fock space. In dimension two, this statement holds after restricting to a codimension-one subspace, as suggested by logarithmic CFT. |
| title | Prefactorization algebras for the conformal Laplacian: Central charge and Hilbert Fock space |
| topic | Mathematical Physics Differential Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2602.17549 |