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Lattice chiral symmetry from bosons in 3+1D

Zhiyao Lu1, Sahand Seifnashri2, and Shu-Heng Shao1

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Phys. Rev. D 114, 034518 – Published 24 August, 2026

DOI: https://doi.org/10.1103/pxvz-r2gf

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.

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Phys. Rev. D 114, 034518– Published 24 August, 2026
  • Received 2 May 2026
  • Accepted 7 August 2026
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