---
title: "Moduli spaces of geometric functorial field theories"
authors:
  - "Jacek Kenig"
  - "Dmitri Pavlov"
year: 2026
venue: "arXiv:math.AT"
arxiv: "2609.11812"
doi: null
source: "https://arxiv.org/abs/2609.11812"
topics:
  - "curiosity"
  - "maths-foundations"
  - "category-theory"
  - "algebraic-topology"
  - "tqft"
seed_rank: 1834
seed_batch: "curiosity-2026-09-15"
reviewed: "2026-09-15"
pool: "maths-foundations"
relevance_score: 9
lineage: geometric-functorial-ft
cites:
  - title: "Moduli spaces of geometric functorial field theories"
    url: "https://arxiv.org/abs/2609.11812"
    year: 2026
    arxiv: "2609.11812"
    doi: null
see: []
---

# Moduli spaces of geometric functorial field theories

## One-sentence takeaway

Moduli of geometric functorial field theories are computed as mapping spaces of O(d)-equivariant simplicial presheaves via Cartesian realization of geometric structures.

## Why it's lovely

Why you might love this: functorial field theories are TQFTs with geometry still attached — Riemannian, conformal, whatever the site encodes. This paper turns their moduli into actual mapping spaces you can compute with, via a Cartesian realization of a geometric structure presheaf. Bridge between Stolz–Teichner dreams and something you can write a spectral-sequence for.

## Key ideas

- Geometric structures as presheaves on smooth families of d-manifolds.
- Cartesian realization → O(d)-equivariant simplicial presheaf.
- Moduli of geometric FFTs ≃ mapping spaces in that equivariant setting.
- Toolkit aimed at computing rather than only defining geometric field theories.

## Caveats

Infrastructure paper; concrete computations of famous moduli (e.g. specific d and F) may be deferred. No safe preexisting Broadside stem for geometric FFT moduli — see left empty.

## Links

- arXiv abs: https://arxiv.org/abs/2609.11812
- PDF: https://arxiv.org/pdf/2609.11812.pdf