Gauss Law, Monodromy Defect, Magnetic Lattice Translation, and Lattice Duality
Abstract
In a Hamiltonian lattice gauge theory, the physical Hilbert space is fixed by the Gauss law, by choosing an eigenspace of the Gauss law operator which generates the gauge transformation. Choosing a non-trivial eigenspace is referred to as the modified Gauss law. In 2+1d dynamical U(1) pure gauge theory, we show that these physical Hilbert spaces are defect Hilbert spaces associated with non-topological monodromy defects for monopole operators and topological defects for U(1) 1-form symmetry, inserted along the time direction. We also construct the corresponding lattice translation operators. Under a nontrivially modified Gauss law, these translations obey a magnetic translation algebra. Finally, we discuss how the modified Gauss laws are manifested in 2+1d compact bosons, via exact duality on the lattice.
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BibTeX
@misc{wei2026gauss,
title = {{Gauss Law, Monodromy Defect, Magnetic Lattice Translation, and Lattice Duality}},
author = {Pengcheng Wei and Yunqin Zheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11417},
eprint = {2609.11417},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11417},
}
RIS
TY - UNPB
TI - Gauss Law, Monodromy Defect, Magnetic Lattice Translation, and Lattice Duality
AU - Pengcheng Wei
AU - Yunqin Zheng
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11417
UR - https://arxiv.org/abs/2609.11417
AB - In a Hamiltonian lattice gauge theory, the physical Hilbert space is fixed by the Gauss law, by choosing an eigenspace of the Gauss law operator which generates the gauge transformation. Choosing a non-trivial eigenspace is referred to as the modified Gauss law. In 2+1d dynamical U(1) pure gauge theory, we show that these physical Hilbert spaces are defect Hilbert spaces associated with non-topological monodromy defects for monopole operators and topological defects for U(1) 1-form symmetry, inserted along the time direction. We also construct the corresponding lattice translation operators. Under a nontrivially modified Gauss law, these translations obey a magnetic translation algebra. Finally, we discuss how the modified Gauss laws are manifested in 2+1d compact bosons, via exact duality on the lattice.
ER -