Solution to the $1+1$ dimensional gauged chiral Fermion problem

We show that the 3450 U(1) chiral fermion theory can appear as the low energy effective field theory of a $1+1\mathrm{D}$ local lattice model of fermions, with an on-site U(1) symmetry and finite-range interactions. The on-site U(1) symmetry means that the U(1) symmetry can be gauged (gaugeable for both background probe and dynamical fields), which leads to a nonperturbative definition of chiral gauge theory—a chiral fermion theory coupled to U(1) gauge theory. Our construction can be generalized to regularize any U(1)-anomaly-free $1+1\mathrm{D}$ gauged chiral fermion theory with a zero chiral central charge (thus no gravitational anomaly) by a lattice, thanks to the recently proven “Poincaré dual” equivalence between the U(1) ’t Hooft anomaly-free condition and the U(1) symmetric interaction gapping rule, via a bosonization-fermionization technique.