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This paper introduces a novel Hamiltonian framework using symmetry disentanglers to construct chiral gauge theories on the lattice without relying on perturbative methods. By transforming non-local symmetries into local ones via constant-depth circuits, it provides an exactly solvable model for specific anomalies and suggests applications to Standard Model hypercharge sectors. The work represents significant theoretical progress in defining fully local, nonperturbative formulations of chiral gauge theories relevant to high-energy physics and quantum simulation.
Chiral Lattice Gauge Theories from Symmetry Disentanglers
arXiv:2601.04304v2 Announce Type: replace-cross Abstract: 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.
Abstract: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.
High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Lattice (hep-lat); Quantum Physics (quant-ph)
arXiv:2601.04304 [hep-th]
(or arXiv:2601.04304v2 [hep-th] for this version)
Full text under the publisher's open licence · 171 words
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