Topological subregions in Chern Simons theory and topological string theory

• URL: http://arxiv.org/abs/2511.08746v1
• Date: Thu, 13 Nov 2025 01:05:25 GMT
• Title: Topological subregions in Chern Simons theory and topological string theory
• Authors: Gabriel Wong,
• Abstract summary: In this work, we appeal to the quantization of Chern Simons theory to define a purely topological notion of a subregion.<n>We develop a diagrammatic calculus for the associated $q$-deformed entanglement entropy, which arise from the entanglement of anyonic edge modes.
• Score: 0.7322349922759154
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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