Derived algebraic geometry of 2d lattice Yang-Mills theory
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909311291097088 |
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| author | Benini, Marco Fernández, Tomás Schenkel, Alexander |
| author_facet | Benini, Marco Fernández, Tomás Schenkel, Alexander |
| contents | A derived algebraic geometric study of classical $\mathrm{GL}_n$-Yang-Mills theory on the $2$-dimensional square lattice $\mathbb{Z}^2$ is presented. The derived critical locus of the Wilson action is described and its local data supported in rectangular subsets $V =[a,b]\times [c,d]\subseteq \mathbb{Z}^2$ with both sides of length $\geq 2$ is extracted. A locally constant dg-category-valued prefactorization algebra on $\mathbb{Z}^2$ is constructed from the dg-categories of perfect complexes on the derived stacks of local data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derived algebraic geometry of 2d lattice Yang-Mills theory Benini, Marco Fernández, Tomás Schenkel, Alexander Mathematical Physics High Energy Physics - Theory Algebraic Geometry 14A30, 70S15, 81T25 A derived algebraic geometric study of classical $\mathrm{GL}_n$-Yang-Mills theory on the $2$-dimensional square lattice $\mathbb{Z}^2$ is presented. The derived critical locus of the Wilson action is described and its local data supported in rectangular subsets $V =[a,b]\times [c,d]\subseteq \mathbb{Z}^2$ with both sides of length $\geq 2$ is extracted. A locally constant dg-category-valued prefactorization algebra on $\mathbb{Z}^2$ is constructed from the dg-categories of perfect complexes on the derived stacks of local data. |
| title | Derived algebraic geometry of 2d lattice Yang-Mills theory |
| topic | Mathematical Physics High Energy Physics - Theory Algebraic Geometry 14A30, 70S15, 81T25 |
| url | https://arxiv.org/abs/2409.06873 |