Topological subregions in Chern Simons theory and topological string theory
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914151597604864 |
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| author | Wong, Gabriel |
| author_facet | Wong, Gabriel |
| contents | The standard, gapped entanglement boundary condition in Chern Simons theory breaks the topological invariance of the theory by introducing a complex structure on the entangling surface. This produces an infinite dimensional subregion Hilbert space, a non-trivial modular Hamiltonion, and a UV-divergent entanglement entropy that is a universal feature of local quantum field theories. In this work, we appeal to the combinatorial quantization of Chern Simons theory to define a purely topological notion of a subregion. The subregion operator algebras are spaces of functions on a quantum group. We develop a diagrammatic calculus for the associated $q$-deformed entanglement entropy, which arise from the entanglement of anyonic edge modes. The $q$-deformation regulates the divergences of the QFT, producing a finite entanglement entropy associated to a $q$-tracial state. We explain how these ideas provide an operator algebraic framework for the entanglement entropy computations in topological string theory \cite{Donnelly:2020teo,Jiang:2020cqo, wongtopstring}, where a large- $N$ limit of the $q$-deformed subregion algebra plays a key role in the stringy description of spacetime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological subregions in Chern Simons theory and topological string theory Wong, Gabriel High Energy Physics - Theory Mathematical Physics Quantum Physics The standard, gapped entanglement boundary condition in Chern Simons theory breaks the topological invariance of the theory by introducing a complex structure on the entangling surface. This produces an infinite dimensional subregion Hilbert space, a non-trivial modular Hamiltonion, and a UV-divergent entanglement entropy that is a universal feature of local quantum field theories. In this work, we appeal to the combinatorial quantization of Chern Simons theory to define a purely topological notion of a subregion. The subregion operator algebras are spaces of functions on a quantum group. We develop a diagrammatic calculus for the associated $q$-deformed entanglement entropy, which arise from the entanglement of anyonic edge modes. The $q$-deformation regulates the divergences of the QFT, producing a finite entanglement entropy associated to a $q$-tracial state. We explain how these ideas provide an operator algebraic framework for the entanglement entropy computations in topological string theory \cite{Donnelly:2020teo,Jiang:2020cqo, wongtopstring}, where a large- $N$ limit of the $q$-deformed subregion algebra plays a key role in the stringy description of spacetime. |
| title | Topological subregions in Chern Simons theory and topological string theory |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2511.08746 |