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PreprintCC BY 4.0arXiv

Moduli spaces of geometric functorial field theories

  • Jacek Kenig
  • Dmitri Pavlov
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Abstract

We develop tools to compute moduli spaces of geometric functorial field theories as mapping spaces of equivariant simplicial presheaves. Given a d-dimensional geometric structure F, presented as a presheaf on the site of smooth families of d-manifolds, we define its Cartesian realization, which is an O(d)-equivariant simplicial presheaf on the site of Cartesian spaces. We use Cartesian realizations to present the moduli space of functorial field theories with geometric structure F as a mapping space between O(d)-equivariant simplicial presheaves. In a companion paper, we use this result to compute the moduli space of smooth one-dimensional oriented Riemannian functorial field theories valued in an arbitrary smooth symmetric monoidal infinity-category.

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Cite

BibTeXRIS
BibTeX
@misc{kenig2026moduli,
  title = {{Moduli spaces of geometric functorial field theories}},
  author = {Jacek Kenig and Dmitri Pavlov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11812},
  eprint = {2609.11812},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11812},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Moduli spaces of geometric functorial field theories
AU  - Jacek Kenig
AU  - Dmitri Pavlov
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11812
UR  - https://arxiv.org/abs/2609.11812
AB  - We develop tools to compute moduli spaces of geometric functorial field theories as mapping spaces of equivariant simplicial presheaves. Given a d-dimensional geometric structure F, presented as a presheaf on the site of smooth families of d-manifolds, we define its Cartesian realization, which is an O(d)-equivariant simplicial presheaf on the site of Cartesian spaces. We use Cartesian realizations to present the moduli space of functorial field theories with geometric structure F as a mapping space between O(d)-equivariant simplicial presheaves. In a companion paper, we use this result to compute the moduli space of smooth one-dimensional oriented Riemannian functorial field theories valued in an arbitrary smooth symmetric monoidal infinity-category.
ER  -