{
  "abstract": "Given a BV theory on a space of fields split into two subspaces (\"infrared\" and \"ultraviolet\"), one has the BV pushforward map $P_*$, sending observables to observables of the effective theory on the infrared space. This note proves that $P_*$ is a quasi-isomorphism of BV complexes, by realizing it as a part of a strong deformation retraction constructed using the homological perturbation lemma. Two proofs are given: (i) comparing Feynman diagrams for $P_*$ with \"cable diagrams\" arising from homological perturbation theory and (ii) using topological quantum mechanics. This construction gives a formula for the quasi-inverse $i_\\mathrm{int}$ of $P_*$ - the map lifting observables of the effective theory to the full theory. The topological quantum mechanics perspective - and its realization as an AKSZ theory - allows one to write $i_\\mathrm{int}$ as a path integral (realizing cable diagrams for $i_\\mathrm{int}$ as Feynman diagrams) and to study its classical limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Lett Math Phys 116, 142 (2026)",
  "arxiv": "2605.30558",
  "author_total": 2,
  "authors": [
    {
      "name": "Alberto S. Cattaneo"
    },
    {
      "name": "Pavel Mnev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3te4tdz42wqnb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.30558",
  "fulltext_url": null,
  "id": "3te4tdz42wqnb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.30558",
  "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",
      "hep-th"
    ],
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      "arxiv",
      "math-ph"
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      "arxiv",
      "math.AT"
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      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7162990673",
  "pdf_url": "https://arxiv.org/pdf/2605.30558",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3te4tdz42wqnb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2605.30558",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.30558"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "BV pushforward as a quasi-isomorphism",
  "title_text": "BV pushforward as a quasi-isomorphism",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/3te4tdz42wqnb",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s11005-026-02149-6",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}