Topological Quantization in Chern-Simons Theory via Quantum Groups and K-Theory — E8 Intelligence Research

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Chern-Simons theory provides a topological quantization framework where the integer level k couples to the gauge group via the quantum group SL(2,Z) action, generating modular tensor categories and linking to K-theory and M2-brane supersymmetry. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22224473

September 1, 2026Open Access

Topological Quantization in Chern-Simons Theory via Quantum Groups and K-Theory — E8 Intelligence Research

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Key Points

Formulate a topological quantization framework in Chern-Simons gauge theory through the mathematical mechanisms of quantum groups, modular tensor categories, and K-theory.
Formulated Chern-Simons actions with quantized level parameter k coupled to the gauge group via modular group SL(2,Z) transformations.
Constructed quantum group representations with deformation parameter q determined by the dual Coxeter number, analyzing conformal blocks via the Verlinde formula.
Mapped differential K-theory pairings across gauge fields using explicit Chern-Simons connection forms.
Level quantization conditions k in Z (or k + h in Z) generate consistent modular tensor categories via modular transformations S and T.
K-theory pairings constructed from Chern-Simons forms establish direct mathematical transitions relevant to M2-brane supersymmetry.

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Implication

Theoretical analysis reveals topological quantization frameworks in Chern-Simons theory, indicating direct links between quantum groups, modular tensor categories, and K-theory.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9935c7636c6408cfa7e334 https://doi.org/10.5281/zenodo.22224473

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Topological Quantization in Chern-Simons Theory via Quantum Groups and K-Theory — E8 Intelligence Research

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Topological Quantization in Chern-Simons Theory via Quantum Groups and K-Theory — E8 Intelligence Research

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