{
  "abstract": "Classical A-polynomials $A(\\ell,m)$ define constraints on coordinates $\\ell$ and $m$ in $SL(2,\\mathbb{C})$ (a complexification of $SU(2)$) character varieties associated to knot complements $S^3\\setminus K$. Quantum A-polynomials $\\hat A(\\hat \\ell,\\hat m)$ are difference operators annihilating Jones polynomials believed to represent wave functions of 3d Chern-Simons theory with gauge group $SU(2)$ on a toroidal pipe surrounding the knot $K$ strand -- a boundary of the knot complement. We suggest a construction of classical shaded A-polynomials $A_a(\\ell_b,m_c)$ associated to Lie groups $SU(N)$, assuming that color $N$ adds some extra \"depth\" and \"shade\" to the classical notion of A-polynomials. We exploit a formalism of Clebsch-Gordan (CG) chords, where indices $a$, $b$, $c$ run over $1,\\ldots,N-1$. CG chords have a natural interpretation in terms of 2d CFTs of WZW type, or in terms of quantum group $U_q(\\mathfrak{su}_N)$. In the case of $\\mathfrak{su}_2$, CG chords could be associated to Reeb chords in a knot contact homology (KCH) framework. KCH suggests its own analogue of A-polynomials, known as augmentation polynomials. The CG chord formalism can be easily extended to arbitrary $\\mathfrak{su}_N$ allowing us to generalize the construction of A(ugmentation)-polynomials to arbitrary $\\mathfrak{su}_N$ and arbitrary representations as well. We primarily aim at classical A-polynomials by considering a double scaling limit in which $q=e^{\\hbar}$, $\\hbar\\to 0$ and the representations are huge: highest weight vector components $w_i\\to \\infty$ while combinations $\\hbar w_i\\sim m_i$ remain finite. We expect the presented techniques will be helpful in deriving quantum A-polynomials for arbitrary Lie (super)algebras $\\mathfrak{g}$. We discuss explicit examples of A-polynomials for knots $3_1$, $4_1$ and $5_1$ for $\\mathfrak{g}=\\mathfrak{su}_3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phys.Rev.D 114 (2026) 6, 066016",
  "arxiv": "2605.22560",
  "author_total": 2,
  "authors": [
    {
      "name": "Dmitry Galakhov"
    },
    {
      "name": "Alexei Morozov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2fsqth91ttgbf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.22560",
  "fulltext_url": null,
  "id": "2fsqth91ttgbf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.22560",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.22560",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2fsqth91ttgbf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2605.22560",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.22560"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Shading A-polynomials via huge representations of $U_q(\\mathfrak{su}_N)$",
  "title_text": "Shading A-polynomials via huge representations of U_q(su_N)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/2fsqth91ttgbf",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/q45y-9mcr",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}