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.
Highlights
The standard model [1,2,3,4,5,6] is a Uð1Þ × SUð2Þ × SUð3Þ gauge theory coupled to fermions that describes all known elementary particles, but until a few years ago, the standard model was only defined perturbatively, and it is well known that such a perturbative expansion does not converge
The reason that the standard model is not a well-defined quantum theory is because the left-hand and right-hand fermions in the standard model carry different Uð1Þ × SUð2Þ representations
One includes proper direct interaction or boson mediated Swift-Smit interactions [31,32] trying to gap out the mirror sector completely, without breaking the gauge symmetry and without affecting the normal sector
Summary
We show that the 3450 U(1) chiral fermion theory can appear as the low energy effective field theory of a 1 þ 1D local lattice model of fermions, with an on-site U(1) symmetry and finite-range interactions. The standard lattice gauge theory approach [8] fails since it cannot produce low energy gauged chiral fermions [9]. [14] pointed out that quantum anomalies are directly connected to and realized at the boundary of topological orders [38] or symmetry protected topological orders [12,13,39] on a lattice in one higher dimension This leads to a classification of anomalies [14,40]. From this point of view, the anomaly-free condition is nothing but the condition for the bulk to be a trivial tensor product state This leads to a solution of the gauged chiral fermion
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