Lattice chiral symmetry from bosons in 3+1d

TL;DR

This paper introduces a solvable lattice Hamiltonian with exact chiral symmetry using bosons, evading no-go theorems, and demonstrating anomaly and higher-form symmetries in the continuum limit.

Contribution

It constructs a lattice model with exact chiral symmetry using bosons, providing a new approach to lattice chiral theories that avoids fermionic no-go theorems.

Findings

Lattice model exhibits exact chiral $U(1)_V imes U(1)_A$ symmetry.

Continuum limit yields a compact boson with axion-like coupling.

Gauging symmetries reveals lattice non-invertible and 2-group symmetries.

Abstract

We present a solvable Hamiltonian that realizes an exact lattice chiral $U(1)_V \times U(1)_A$ 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 axion-like 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 non-invertible and 2-group symmetries, respectively, matching the continuum picture.