Chiral Lattice Gauge Theories from Symmetry Disentanglers
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914239379144704 |
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| author | Thorngren, Ryan Preskill, John Fidkowski, Lukasz |
| author_facet | Thorngren, Ryan Preskill, John Fidkowski, Lukasz |
| contents | We propose a Hamiltonian framework for constructing chiral gauge theories on the lattice based on symmetry disentanglers: constant-depth circuits of local unitaries that transform not-on-site symmetries into on-site ones. When chiral symmetry can be realized not-on-site and such a disentangler exists, the symmetry can be implemented in a strictly local Hamiltonian and gauged by standard lattice methods. Using lattice rotor models, we realize this idea in 1+1 and 3+1 spacetime dimensions for $U(1)$ symmetries with mixed 't Hooft anomalies, and show that symmetry disentanglers can be constructed when anomalies cancel. As an example, we present an exactly solvable Hamiltonian lattice model of the (1+1)-dimensional "3450" chiral gauge theory, and we argue that a related construction applies to the $U(1)$ hypercharge symmetry of the Standard Model fermions in 3+1 dimensions. Our results open a new route toward fully local, nonperturbative formulations of chiral gauge theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04304 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Chiral Lattice Gauge Theories from Symmetry Disentanglers Thorngren, Ryan Preskill, John Fidkowski, Lukasz High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Lattice Quantum Physics We propose a Hamiltonian framework for constructing chiral gauge theories on the lattice based on symmetry disentanglers: constant-depth circuits of local unitaries that transform not-on-site symmetries into on-site ones. When chiral symmetry can be realized not-on-site and such a disentangler exists, the symmetry can be implemented in a strictly local Hamiltonian and gauged by standard lattice methods. Using lattice rotor models, we realize this idea in 1+1 and 3+1 spacetime dimensions for $U(1)$ symmetries with mixed 't Hooft anomalies, and show that symmetry disentanglers can be constructed when anomalies cancel. As an example, we present an exactly solvable Hamiltonian lattice model of the (1+1)-dimensional "3450" chiral gauge theory, and we argue that a related construction applies to the $U(1)$ hypercharge symmetry of the Standard Model fermions in 3+1 dimensions. Our results open a new route toward fully local, nonperturbative formulations of chiral gauge theories. |
| title | Chiral Lattice Gauge Theories from Symmetry Disentanglers |
| topic | High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Lattice Quantum Physics |
| url | https://arxiv.org/abs/2601.04304 |