Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Kenig, Jacek, Pavlov, Dmitri
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212233919