Lattice chiral symmetry from bosons in 3+1d

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.

Comments: 32 pages plus appendices. 8 figures