Twisted scattering from Chern-Simons theory
Abstract
We consider boundary conditions of two-dimensional Dirac fermions which preserve a non-anomalous continuous symmetry which acts differently on the left- and right-movers. Such boundaries are equivalent to topological defects of Weyl fermions preserving the symmetry. We give a general construction of such defects for conformally-embedded symmetries using Chern-Simons theory. They always exist and can be realised as half-space gauging defects for some finite categorical symmetry. Using this technology, we compute the twist lines to which fermions become attached upon scattering through the defect, the boundary central charge of the corresponding folded boundary state, and its mod-2 valued SPT class. As applications, we first consider abelian symmetries and find agreement with known results in the literature. We then study a novel example where an SU(2) × SU(4) × U(1)2 symmetry is preserved. In contrast to the abelian case, the twist lines are intrinsically non-invertible and belong to either a TY(ℤ3 × ℤ3) or Rep(𝕊3) × ℤ3 symmetry depending on whether scattering is to the left or the right.
Related
- Chiral edge modes from lattice Chern-Simons theory
- A Functorial Theory of Defects in Abelian Chern-Simons Theory
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- Regular-Zero Drinfeld-Sokolov Charges in Doubled Four-Dimensional Chern-Simons Theory
- Edge physics and the Casimir interaction in Maxwell-Chern-Simons theory on a strip
BibTeX
@misc{ariastamargo2026twisted,
title = {{Twisted scattering from Chern-Simons theory}},
author = {Guillermo Arias-Tamargo and Philip Boyle Smith and Rishi Mouland and Max Velásquez Cotini Hutt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30232},
eprint = {2610.30232},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30232},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Twisted scattering from Chern-Simons theory
AU - Guillermo Arias-Tamargo
AU - Philip Boyle Smith
AU - Rishi Mouland
AU - Max Velásquez Cotini Hutt
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30232
UR - https://arxiv.org/abs/2610.30232
AB - We consider boundary conditions of two-dimensional Dirac fermions which preserve a non-anomalous continuous symmetry which acts differently on the left- and right-movers. Such boundaries are equivalent to topological defects of Weyl fermions preserving the symmetry. We give a general construction of such defects for conformally-embedded symmetries using Chern-Simons theory. They always exist and can be realised as half-space gauging defects for some finite categorical symmetry. Using this technology, we compute the twist lines to which fermions become attached upon scattering through the defect, the boundary central charge of the corresponding folded boundary state, and its mod-2 valued SPT class. As applications, we first consider abelian symmetries and find agreement with known results in the literature. We then study a novel example where an SU(2) × SU(4) × U(1)^2 symmetry is preserved. In contrast to the abelian case, the twist lines are intrinsically non-invertible and belong to either a TY(ℤ_3 × ℤ_3) or Rep(𝕊_3) × ℤ_3 symmetry depending on whether scattering is to the left or the right.
ER -