A Functorial Theory of Defects in Abelian Chern-Simons Theory
Abstract
Recent work has constructed Abelian Chern-Simons theories as categorical TQFTs, allowing us to naturally incorporate categorical defects and construct defect extensions of Abelian Chern-Simons TQFTs. We first identify the Turaev-Viro realizations of Abelian Chern-Simons theory in the center and doubled pointed modular cases, clarifying the distinction between single bulk realizations and canonical doubled ones. Then we obtain Turaev-Viro partition functions in terms of Reidemeister-torsion densities. Alternatively, the Alterfold construction supplies the associated topological boundaries, domain walls, and condensation sectors, establishing an explicit Alterfold/Chern-Simons dictionary. We show that the finite quadratic module is the invariant controlling the bulk theory, its topological symmetries, orientation-reversal invariance, and defects. We further show that multicomponent Abelian BF theory arises as the extended TQFT of an off-diagonal Abelian Chern-Simons theory, placing it naturally within the same extended framework. Finally, we demonstrate that recently proposed Abelian Chern-Simons dualities do not define a genuine TQFT duality. These results provide a concrete model for defects in Abelian topological orders and suggest a route toward the non-Abelian case.
Related
- Chiral edge modes from lattice Chern-Simons theory
- Regular-Zero Drinfeld-Sokolov Charges in Doubled Four-Dimensional Chern-Simons Theory
- Large-Level Limit of Doubled Chern-Simons Theory Part I: Regular Sector, Boundaries and Interfaces
- Higher abelian gauge theory in BV formalism
- Skein theory, line defects, and quantum symmetric pairs
BibTeX
@misc{galviz2026functorial,
title = {{A Functorial Theory of Defects in Abelian Chern-Simons Theory}},
author = {Daniel Galviz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.21414},
eprint = {2609.21414},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21414},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Functorial Theory of Defects in Abelian Chern-Simons Theory
AU - Daniel Galviz
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2609.21414
UR - https://arxiv.org/abs/2609.21414
AB - Recent work has constructed Abelian Chern-Simons theories as categorical TQFTs, allowing us to naturally incorporate categorical defects and construct defect extensions of Abelian Chern-Simons TQFTs. We first identify the Turaev-Viro realizations of Abelian Chern-Simons theory in the center and doubled pointed modular cases, clarifying the distinction between single bulk realizations and canonical doubled ones. Then we obtain Turaev-Viro partition functions in terms of Reidemeister-torsion densities. Alternatively, the Alterfold construction supplies the associated topological boundaries, domain walls, and condensation sectors, establishing an explicit Alterfold/Chern-Simons dictionary. We show that the finite quadratic module is the invariant controlling the bulk theory, its topological symmetries, orientation-reversal invariance, and defects. We further show that multicomponent Abelian BF theory arises as the extended TQFT of an off-diagonal Abelian Chern-Simons theory, placing it naturally within the same extended framework. Finally, we demonstrate that recently proposed Abelian Chern-Simons dualities do not define a genuine TQFT duality. These results provide a concrete model for defects in Abelian topological orders and suggest a route toward the non-Abelian case.
ER -