Juven Wang, Xiao-Gang Wen
A non-perturbative definition of anomaly-free chiral fermions and bosons in 1+1D spacetime as finite quantum systems on 1D lattice is proposed. In particular, we show that the 3-5-4-0 chiral fermion theory, with two left-moving fermions of charge-3 and charge-4, and two right-moving fermions of charge-5 and charge-0 at low energy, can be put on a 1D spatial lattice without breaking the U(1) symmetry, if we include strong interactions between fermions. In general, we show that any 1+1D anomaly-free chiral matter theory (satisfying 't Hooft anomaly matching condition) can be defined as finite quantum systems on 1D lattice with on-site symmetry, if we include strong interactions between matter fields. Our approach provides another way, apart from Ginsparg-Wilson fermions approach, to avoid Nielsen-Ninomiya theorem's fermion-doubling challenge. As an additional remark, we prove the equivalence relation between 't Hooft anomaly matching condition and the boundary fully gapping rules.
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http://arxiv.org/abs/1307.7480
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