Loop observables for BF theories in any dimension and the cohomology of knots

TL;DR

This paper introduces a generalized class of loop observables for BF theories across all dimensions, linking their expectation values to knot cohomology, and explores a trivalent interaction theory resembling 3D Chern-Simons.

Contribution

It extends Wilson loop observables to BF theories in any dimension within the BV framework and connects their expectation values to knot cohomology classes.

Findings

Expectation values form cohomology classes of imbeddings of a circle.

A trivalent interaction theory similar to 3D Chern-Simons is constructed.

The framework applies uniformly across different dimensions.

Abstract

A generalization of Wilson loop observables for BF theories in any dimension is introduced in the Batalin-Vilkovisky framework. The expectation values of these observables are cohomology classes of the space of imbeddings of a circle. One of the resulting theories discussed in the paper has only trivalent interactions and, irrespective of the actual dimension, looks like a 3-dimensional Chern-Simons theory.