Lattice chiral symmetry from bosons in 3 + 1 D
Abstract
We present a solvable Hamiltonian that realizes an exact lattice chiral U ( 1 ) V × U ( 1 ) A symmetry. Nielsen-Ninomiya-type no-go theorems are evaded by using lattice bosons rather than fermions. The continuum limit is a compact boson field theory with an axionlike coupling. The U ( 1 ) V symmetry shifts the scalar, while U ( 1 ) A acts on local operators associated with short axion strings and is transmuted into a higher-form symmetry in the continuum limit. We demonstrate the chiral anomaly by showing that the lattice theta angle is shifted by an axial rotation when U ( 1 ) V is gauged. Gauging either U ( 1 ) V or U ( 1 ) A leads to lattice noninvertible and 2-group symmetries, respectively, matching the continuum picture.
Fields of Study & Subjects
Quantum Chromodynamics and Particle Interactions
Quantum Mechanics and Non-Hermitian Physics
Nuclear physics research studies
Publication details
- Journal / source
- Physical review. D/Physical review. D.
- Publisher
- American Physical Society (APS)
- Volume
- 114
- Issue
- 3
- Publication date
- 7 August 2026
- Language
- EN