{
  "abstract": "For a holomorphic vector bundle $F$ of rank $r$ on a smooth Riemann surface $X$ we construct a trace map on the chiral homology of the chiral Clifford algebra $\\CE$ attached to the purely odd bundle $E=Π(F\\oplus F^\\vee\\otimesω_X)$. It is the chiral-algebraic realization of the rank two fermionic vertex operator superalgebra. The free fermion (bc-type) conformal field theory built from a dual pair of odd fields $ β_i\\in F$, $γ^j\\in F^\\vee\\otimesω_X$. We give a complete construction of this vertex operator superalgebra, its associated vertex superalgebra bundle, and the isomorphism between the latter's chiral algebra and the chiral envelope $\\CE$. Using the Batalin-Vilkovisky (BV) formalism together with Feynman diagrams we prove that the resulting trace map \\[ \\Trch : \\bigl(\\widetilde\\sC^{\\ch}(X,\\CE)_{\\sQ},\\, \\dch_{\\CE}\\bigr)\\longrightarrow (\\OBV,-\\DBV) \\] is a chain map satisfying a generalized quantum master equation and is a quasi-isomorphism, generalizing to the odd/Clifford setting the trace map on chiral Weyl algebras constructed by Gui for symplectic bosons. We establish existence, homotopy uniqueness, and functoriality (including metric-independence up to chain homotopy) of the trace map, prove cyclicity of the relevant supertrace, and verify nilpotency of $\\DBV$, the graded Leibniz rule, $d^2=0$ for every differential introduced. As an application we compute the trace map on a modified affine current and on a modified energy-momentum tensor, recovering, purely algebraically from the chiral chain complex, Fay's classical formulas for the variation of the fermionic (Ray-Singer) analytic torsion along the moduli of the bundle $F$ and along the moduli of the curve $X$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.02065",
  "author_total": 1,
  "authors": [
    {
      "name": "A. Zuevsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7142d99hkzqx9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.02065",
  "fulltext_url": null,
  "id": "7142d99hkzqx9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.02065",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7172463219",
  "pdf_url": "https://arxiv.org/pdf/2608.02065",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7142d99hkzqx9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2608.02065",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.02065"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Trace maps on chiral Clifford algebras for the rank two fermionic vertex operator superalgebra",
  "title_text": "Trace maps on chiral Clifford algebras for the rank two fermionic vertex operator superalgebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/7142d99hkzqx9",
  "venue": "arXiv",
  "versions": []
}