A bosonic lattice model realizes exact chiral symmetry and its anomaly in 3+1d, with the continuum limit a compact boson theory with axion-like coupling.
Friedan,A PROOF OF THE NIELSEN-NINOMIYA THEOREM,Commun
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Lattice chiral symmetry from bosons in 3+1d
A bosonic lattice model realizes exact chiral symmetry and its anomaly in 3+1d, with the continuum limit a compact boson theory with axion-like coupling.