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arXiv · 2609.11812

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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Jacek Kenig, Dmitri Pavlov. 2026-09-10. Moduli spaces of geometric functorial field theories. https://arxiv.org/abs/2609.11812

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