PreprintCC BY 4.0arXiv
Chiral edge modes from lattice Chern-Simons theory
Abstract
It is shown that a level k Abelian lattice Chern-Simons theory with continuum time and a spatial square lattice, which is a topological field theory on the latticized plane and torus, when quantized on a spatial cylinder reduces to chiral edge excitations, exactly localized on the two boundaries and carrying two commuting lattice versions of the level-k U(1) Kac-Moody algebra of opposite chirality. The algebras are represented on a Fock space in the noncompact theory and by a finite Weyl algebra in the compact one. We also observe that the theory has a natural framing of Wilson loops which exhibits the correct framing anomaly.
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BibTeX
@misc{semenoff2026chiral,
title = {{Chiral edge modes from lattice Chern-Simons theory}},
author = {Gordon W. Semenoff},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05663},
eprint = {2611.05663},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05663},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Chiral edge modes from lattice Chern-Simons theory
AU - Gordon W. Semenoff
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05663
UR - https://arxiv.org/abs/2611.05663
AB - It is shown that a level k Abelian lattice Chern-Simons theory with continuum time and a spatial square lattice, which is a topological field theory on the latticized plane and torus, when quantized on a spatial cylinder reduces to chiral edge excitations, exactly localized on the two boundaries and carrying two commuting lattice versions of the level-k U(1) Kac-Moody algebra of opposite chirality. The algebras are represented on a Fock space in the noncompact theory and by a finite Weyl algebra in the compact one. We also observe that the theory has a natural framing of Wilson loops which exhibits the correct framing anomaly.
ER -