Large-Level Limit of Doubled Chern-Simons Theory Part I: Regular Sector, Boundaries and Interfaces
Abstract
We study three-dimensional BF theory as the large-level limit of the doubled Chern--Simons theory Gk× G−k for simply connected, compact, simple G, a limit that connects the symmetry topological field theories of finite and continuous symmetries. Lines whose two highest weights grow linearly with k at fixed difference become BF lines, with magnetic flux set by their average and electric charge equal to their difference. Representing level-k torus states as normalized flux--charge wave packets, we prove that every fixed modular transformation of any fixed normalizable state with regular flux converges in the strong-* topology to its BF counterpart. The Dehn twist gives each line exactly its Aharonov--Bohm phase at every level, while S converges to a Fourier transform exchanging flux and charge, without escaping to singular holonomies or large charges. States that approach singular fluxes at large k are not covered. The natural boundary 2d theory is speculated to be a decompactified boson in the abelian case G=U(1), and dim G non-compact free scalars for general G. For SU(2), we discuss the gapped interfaces between adjacent levels, which must shift some flux or charge by a finite amount. In the k→∞ limit the interface is conjectured to be the c=1 Runkel--Watts theory.
Related
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- Failure of dimension drop for harmonic measure on Ahlfors regular boundaries of dimension close to $1$
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BibTeX
@misc{guan2026largelevel,
title = {{Large-Level Limit of Doubled Chern-Simons Theory Part I: Regular Sector, Boundaries and Interfaces}},
author = {Shengyi Guan and Qiang Jia and Jiahua Tian and Yi-Nan Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26735},
eprint = {2610.26735},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26735},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Large-Level Limit of Doubled Chern-Simons Theory Part I: Regular Sector, Boundaries and Interfaces
AU - Shengyi Guan
AU - Qiang Jia
AU - Jiahua Tian
AU - Yi-Nan Wang
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26735
UR - https://arxiv.org/abs/2610.26735
AB - We study three-dimensional BF theory as the large-level limit of the doubled Chern--Simons theory G_k× G_−k for simply connected, compact, simple G, a limit that connects the symmetry topological field theories of finite and continuous symmetries. Lines whose two highest weights grow linearly with k at fixed difference become BF lines, with magnetic flux set by their average and electric charge equal to their difference. Representing level-k torus states as normalized flux--charge wave packets, we prove that every fixed modular transformation of any fixed normalizable state with regular flux converges in the strong-* topology to its BF counterpart. The Dehn twist gives each line exactly its Aharonov--Bohm phase at every level, while S converges to a Fourier transform exchanging flux and charge, without escaping to singular holonomies or large charges. States that approach singular fluxes at large k are not covered. The natural boundary 2d theory is speculated to be a decompactified boson in the abelian case G=U(1), and dim G non-compact free scalars for general G. For SU(2), we discuss the gapped interfaces between adjacent levels, which must shift some flux or charge by a finite amount. In the k→∞ limit the interface is conjectured to be the c=1 Runkel--Watts theory.
ER -