Algebras over not too little discs
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914304181141504 |
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| author | Calaque, Damien Carmona, Victor |
| author_facet | Calaque, Damien Carmona, Victor |
| contents | By the introduction of locally constant prefactorization algebras at a fixed scale, we show a mathematical incarnation of the fact that observables at a given scale of a topological field theory propagate to every scale over euclidean spaces. The key is that these prefactorization algebras over $\mathbb{R}^n$ are equivalent to algebras over the little $n$-disc operad. For topological field theories with defects, we get analogous results by replacing $\mathbb{R}^n$ with the spaces modelling corners $\mathbb{R}^p\times\mathbb{R}^{q}_{\geq 0}$. As a toy example in $1d$, we quantize, once more, constant Poisson structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18192 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebras over not too little discs Calaque, Damien Carmona, Victor Algebraic Topology Mathematical Physics Quantum Algebra 18N70, 18N60, 18M75, 18M70, 81T70, 81S99 By the introduction of locally constant prefactorization algebras at a fixed scale, we show a mathematical incarnation of the fact that observables at a given scale of a topological field theory propagate to every scale over euclidean spaces. The key is that these prefactorization algebras over $\mathbb{R}^n$ are equivalent to algebras over the little $n$-disc operad. For topological field theories with defects, we get analogous results by replacing $\mathbb{R}^n$ with the spaces modelling corners $\mathbb{R}^p\times\mathbb{R}^{q}_{\geq 0}$. As a toy example in $1d$, we quantize, once more, constant Poisson structures. |
| title | Algebras over not too little discs |
| topic | Algebraic Topology Mathematical Physics Quantum Algebra 18N70, 18N60, 18M75, 18M70, 81T70, 81S99 |
| url | https://arxiv.org/abs/2407.18192 |