Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 1 h ago
PreprintCC BY 4.0arXiv

BV pushforward as a quasi-isomorphism

  • Alberto S. Cattaneo
  • Pavel Mnev
Open at sourcePDFDOICite

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 iint 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 iint as a path integral (realizing cable diagrams for iint as Feynman diagrams) and to study its classical limit.

Versions

Related

  1. Classical BV Pushforward
    Xin Geng, Andrey Losev, Vyacheslav Lysov
    arXivPreprintarXiv licenceFull textMathematical physicsHigh-energy & particle physicsarXiv
  2. A Quadratically Enriched Pushforward for Deligne--Mumford Stacks
    Candace Bethea, Kirsten Wickelgren
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv
  3. Pushforward dynamics on Wasserstein spaces and measure rigidity
    Douglas Finamore, André Magalhães de Sá Gomes, Christian S. Rodrigues
    arXivPreprintCC BY 4.0Full textDynamical systemsGeometry & topologyarXiv
  4. Intrinsic Gradient Barriers in Pushforward Deep Generative Models
    Edric Tam, Qingyang Liu, Barbara Engelhardt +1
    arXivPreprintCC BY 4.0Full textStatisticsarXiv
  5. Branched Itô formula and natural Itô-Stratonovich isomorphism
    Carlo Bellingeri, Emilio Ferrucci, Nikolas Tapia
    Advances in MathematicsPeer-reviewedLicence not statedFull text1 citedProbabilityHAL

Cite

BibTeXRIS
BibTeX
@misc{cattaneo2026pushforward,
  title = {{BV pushforward as a quasi-isomorphism}},
  author = {Alberto S. Cattaneo and Pavel Mnev},
  howpublished = {arXiv},
  year = {2026},
  month = jun,
  doi = {10.48550/arxiv.2605.30558},
  eprint = {2605.30558},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.30558},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - BV pushforward as a quasi-isomorphism
AU  - Alberto S. Cattaneo
AU  - Pavel Mnev
PY  - 2026
DA  - 2026/06/08
PB  - arXiv
DO  - 10.48550/arxiv.2605.30558
UR  - https://arxiv.org/abs/2605.30558
AB  - 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_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_int as a path integral (realizing cable diagrams for i_int as Feynman diagrams) and to study its classical limit.
ER  -