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

TL;DR

This paper presents a lattice model that realizes a 1+1D U(1) chiral fermion theory with on-site symmetry, enabling a non-perturbative gauge-invariant formulation of chiral gauge theories.

Contribution

It introduces a lattice construction for 1+1D gauged chiral fermion theories with on-site symmetry, extending to anomaly-free cases with zero chiral central charge.

Findings

Realizes a 1+1D chiral fermion theory as a low-energy limit of a lattice model.

Enables non-perturbative definition of chiral gauge theories with on-site symmetry.

Generalizes to all U(1)-anomaly-free 1+1D gauged chiral fermion theories with zero chiral central charge.

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.