A note on abelian arithmetic BF-theory

TL;DR

This paper computes arithmetic path integrals in abelian BF-theory over totally imaginary fields, linking them to natural arithmetic invariants of algebraic structures like $\

Contribution

It introduces a novel approach to connect arithmetic invariants with path integrals in abelian BF-theory over number rings.

Findings

Arithmetic path integrals evaluate to invariants of algebraic structures.

Connections established between BF-theory and arithmetic invariants.

Provides explicit computations over totally imaginary fields.

Abstract

We compute some arithmetic path integrals for BF-theory over the ring of integers of a totally imaginary field, which evaluate to natural arithmetic invariants associated to $\mathbb{G}_m$ and abelian varieties.