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

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arxiv 1807.05998 v3 pith:J2LLATQE submitted 2018-07-16 hep-lat cond-mat.str-elhep-phhep-th

Juven Wang , Xiao-Gang Wen This is my paper · ORCID
classification hep-latcond-mat.str-elhep-phhep-th
keywords chiraltheoryfermiongaugedsymmetryanomalygaugelattice
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Exactly Solvable 1+1d Chiral Lattice Gauge Theories

    hep-th 2026-01 conditional novelty 7.0 of 10

    Anomaly-free chiral U(1) gauge theories in 1+1 dimensions can be written as quadratic, exactly solvable lattice Hamiltonians, with the 34-50 model as an explicit example.

  2. Ginsparg-Wilson Hamiltonians with Improved Chiral Symmetry

    hep-lat 2025-05 conditional novelty 7.0 of 10

    A tunable family of Ginsparg-Wilson Hamiltonians is constructed in which the chiral charge becomes progressively more quantized as k increases, though locality degrades.

  3. Unpaired Weyl fermion on an axion string in a finite lattice

    hep-th 2025-06 conditional novelty 6.0 of 10

    A modified crossed-domain-wall axion string on an N=28 periodic lattice produces an unpaired, single-chirality Weyl fermion branch, extending the Kaplan-Sen disk construction to string defects.

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