Deformation Quantization via Categorical Factorization Homology
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912991074582528 |
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| author | Karlsson, Eilind Keller, Corina Müller, Lukas Pulmann, Ján |
| author_facet | Karlsson, Eilind Keller, Corina Müller, Lukas Pulmann, Ján |
| contents | This paper develops an approach to categorical deformation quantization via factorization homology. We show that a quantization of the local coefficients for factorization homology is equivalent to consistent quantizations of its value on manifolds. To formulate our results we introduce the concepts of shifted almost Poisson and BD categories. Our main example is the character stack of flat principal bundles for a reductive algebraic group $G$, where we show that applying the general framework to the Drinfeld category reproduces deformations previously introduced by Li-Bland and Ševera. As a direct consequence, we can conclude a precise relation between their quantization and those introduced by Alekseev, Grosse, and Schomerus. To arrive at our results we compute factorization homology with values in a ribbon category enriched over complete $\mathbb{C}[[\hbar]]$-modules. More generally, we define enriched skein categories which compute factorization homology for ribbon categories enriched over a general closed symmetric monoidal category $\mathcal{V}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12516 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deformation Quantization via Categorical Factorization Homology Karlsson, Eilind Keller, Corina Müller, Lukas Pulmann, Ján Quantum Algebra Mathematical Physics Algebraic Topology Symplectic Geometry This paper develops an approach to categorical deformation quantization via factorization homology. We show that a quantization of the local coefficients for factorization homology is equivalent to consistent quantizations of its value on manifolds. To formulate our results we introduce the concepts of shifted almost Poisson and BD categories. Our main example is the character stack of flat principal bundles for a reductive algebraic group $G$, where we show that applying the general framework to the Drinfeld category reproduces deformations previously introduced by Li-Bland and Ševera. As a direct consequence, we can conclude a precise relation between their quantization and those introduced by Alekseev, Grosse, and Schomerus. To arrive at our results we compute factorization homology with values in a ribbon category enriched over complete $\mathbb{C}[[\hbar]]$-modules. More generally, we define enriched skein categories which compute factorization homology for ribbon categories enriched over a general closed symmetric monoidal category $\mathcal{V}$. |
| title | Deformation Quantization via Categorical Factorization Homology |
| topic | Quantum Algebra Mathematical Physics Algebraic Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2410.12516 |