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arXiv · 1807.05998

A Solution to the 1+1D Gauged Chiral Fermion Problem

Juven Wang·Xiao-Gang Wen
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Abstract

We show that the 3450 U(1) chiral fermion theory can appear as the low energy effective field theory of a 1+1D local lattice model, 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 non-perturbative 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+1D gauged chiral fermion theory with a zero chiral central charge (thus no gravitational anomaly) by a lattice, thanks to the recently proven "Poincar\'e dual" equivalence between the U(1) 't Hooft anomaly free condition and the U(1) symmetric interaction gapping rule, via a bosonization-fermionization technique.

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Juven Wang, Xiao-Gang Wen. 2018-07-16. A Solution to the 1+1D Gauged Chiral Fermion Problem. https://doi.org/10.1103/physrevd.99.111501

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