{
  "abstract": "A lattice Dirac operator designed to preserve exact chiral symmetry by weighting the derivative with a quenched random field---the \\emph{chiral disordered fermions} (\\CDF) of [L.\\ Jacobs, Phys.\\ Rev.\\ Lett.\\ \\textbf{51}, 172 (1983)]---is reexamined with modern tools. We show that the disorder-averaged operator satisfies $\\anticomm{\\Deff}{\\gfive}=0$ exactly, to all orders in disorder strength. Disorder lifts the doubler degeneracy, driving doublers off the real axis into a complex mass while the physical mode remains protected, but does so through non-Hermiticity rather than a Ginsparg--Wilson relation. Consequently the axial index vanishes in every formulation: the Hermitian trace $\\Tr(\\gfive D)$, the bi-orthogonal index for non-Hermitian operators, and the algebraic Riesz-projector index, including at exceptional points. The \\CDF operator therefore cannot reproduce the axial anomaly: its failure is enforced by the exact chiral symmetry it preserves. We classify neighboring constructions by the Dirac channel carrying the lattice structure. Disorder in the $\\g_μ$ channel preserves chirality, realizes an Altland--Zirnbauer chiral class, and cannot carry an index; disorder in the $\\mathbb{1}$ mass channel breaks chiral symmetry and yields Callan--Harvey/domain-wall physics. A one-parameter family interpolates between them, with the 1983 operator and Kaplan's domain wall as opposite limits, distinguished not by disorder itself but by the channel it occupies. This unifies lattice-QCD undoubling with the tenfold-way classification of disordered Dirac fermions and settles the disorder route to chiral lattice fermions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05395",
  "author_total": 1,
  "authors": [
    {
      "name": "Laurence A. Jacobs"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1d0j630phnnhr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05395",
  "fulltext_url": null,
  "id": "1d0j630phnnhr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05395",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.other"
    ],
    [
      "arxiv",
      "hep-lat"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05395",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1d0j630phnnhr.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.05395",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05395"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.other",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    }
  ],
  "title": "Exact chiral symmetry, non-Hermiticity, and the axial anomaly on the lattice: A symmetry-class criterion for disorder-induced undoubling",
  "title_text": "Exact chiral symmetry, non-Hermiticity, and the axial anomaly on the lattice: A symmetry-class criterion for disorder-induced undoubling",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:10Z",
  "url": "https://research.draconitic.com/paper/1d0j630phnnhr",
  "venue": "arXiv",
  "versions": []
}