Topological Aspects of the c=2 Model in the Continuum and on the Lattice
Abstract
We discuss the continuum two-dimensional conformal field theory, whose target space is a two-torus. In addition to its standard zero-form internal symmetries, the model also has a −1-form symmetry associated with its θ-parameter, which is also known as a background B-field. These symmetries combine into a higher group with anomalies. A spatially winding B-field generically breaks the spatial translation symmetry completely, and reduces the continuous target-space (internal) momentum symmetry to a (projectively realized) discrete subgroup. When B varies linearly, a discrete translation subgroup survives, and it combines with the internal symmetry into a non-Abelian group, while the other translations survive as non-invertible symmetries. Even though the model lacks the standard spatial translation symmetry, the non-invertible translation symmetry explains why it is solvable via a Fourier decomposition. We then consider a lattice version of this system, using its modified Villain formulation. Surprisingly, all these subtleties in the symmetries of the continuum model exist on a finite lattice. Finally, we discuss various generalizations of this model, demonstrating that the phenomena we uncovered are more broadly valid.
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BibTeX
@misc{choi2026topological,
title = {{Topological Aspects of the $c=2$ Model in the Continuum and on the Lattice}},
author = {Yichul Choi and Nathan Seiberg and Sahand Seifnashri and Wucheng Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22485},
eprint = {2610.22485},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22485},
}
RIS
TY - UNPB
TI - Topological Aspects of the c=2 Model in the Continuum and on the Lattice
AU - Yichul Choi
AU - Nathan Seiberg
AU - Sahand Seifnashri
AU - Wucheng Zhang
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22485
UR - https://arxiv.org/abs/2610.22485
AB - We discuss the continuum two-dimensional conformal field theory, whose target space is a two-torus. In addition to its standard zero-form internal symmetries, the model also has a −1-form symmetry associated with its θ-parameter, which is also known as a background B-field. These symmetries combine into a higher group with anomalies. A spatially winding B-field generically breaks the spatial translation symmetry completely, and reduces the continuous target-space (internal) momentum symmetry to a (projectively realized) discrete subgroup. When B varies linearly, a discrete translation subgroup survives, and it combines with the internal symmetry into a non-Abelian group, while the other translations survive as non-invertible symmetries. Even though the model lacks the standard spatial translation symmetry, the non-invertible translation symmetry explains why it is solvable via a Fourier decomposition. We then consider a lattice version of this system, using its modified Villain formulation. Surprisingly, all these subtleties in the symmetries of the continuum model exist on a finite lattice. Finally, we discuss various generalizations of this model, demonstrating that the phenomena we uncovered are more broadly valid.
ER -