Topological subregions in Chern Simons theory and topological string theory
Gabriel Wong

TL;DR
This paper introduces a topological approach to defining subregions in Chern-Simons theory, using quantum groups and diagrammatic calculus to obtain finite entanglement entropy, with implications for topological string theory.
Contribution
It develops a purely topological framework for subregion entanglement in Chern-Simons theory using quantum group functions and $q$-deformation, avoiding UV divergences.
Findings
Defined a topological notion of subregion using quantum group functions.
Developed a diagrammatic calculus for $q$-deformed entanglement entropy.
Produced finite entanglement entropy via $q$-deformation, linking to topological string theory.
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 -deformed entanglement entropy, which arise from the entanglement of anyonic edge modes. The -deformation regulates the divergences of the QFT, producing a finite entanglement entropy associated to a -tracial state. We explain how these…
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Taxonomy
TopicsQuantum many-body systems · Black Holes and Theoretical Physics · Topological Materials and Phenomena
