Quantization of derived cotangent stacks and gauge theory on directed graphs
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913433327239168 |
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| author | Benini, Marco Pridham, Jonathan P. Schenkel, Alexander |
| author_facet | Benini, Marco Pridham, Jonathan P. Schenkel, Alexander |
| contents | We study the quantization of the canonical unshifted Poisson structure on the derived cotangent stack $T^\ast[X/G]$ of a quotient stack, where $X$ is a smooth affine scheme with an action of a (reductive) smooth affine group scheme $G$. This is achieved through an {é}tale resolution of $T^\ast[X/G]$ by stacky CDGAs that allows for an explicit description of the canonical Poisson structure on $T^\ast[X/G]$ and of the dg-category of modules quantizing it. These techniques are applied to construct a dg-category-valued prefactorization algebra that quantizes a gauge theory on directed graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2201_10225 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantization of derived cotangent stacks and gauge theory on directed graphs Benini, Marco Pridham, Jonathan P. Schenkel, Alexander Mathematical Physics High Energy Physics - Theory Algebraic Geometry Quantum Algebra 14A30, 14D23, 53D55, 81Txx We study the quantization of the canonical unshifted Poisson structure on the derived cotangent stack $T^\ast[X/G]$ of a quotient stack, where $X$ is a smooth affine scheme with an action of a (reductive) smooth affine group scheme $G$. This is achieved through an {é}tale resolution of $T^\ast[X/G]$ by stacky CDGAs that allows for an explicit description of the canonical Poisson structure on $T^\ast[X/G]$ and of the dg-category of modules quantizing it. These techniques are applied to construct a dg-category-valued prefactorization algebra that quantizes a gauge theory on directed graphs. |
| title | Quantization of derived cotangent stacks and gauge theory on directed graphs |
| topic | Mathematical Physics High Energy Physics - Theory Algebraic Geometry Quantum Algebra 14A30, 14D23, 53D55, 81Txx |
| url | https://arxiv.org/abs/2201.10225 |