Operator Spin Foams: holonomy formulation and coarse graining

TL;DR

This paper introduces a dual holonomy formulation of operator spin foam models, facilitating coarse graining and renormalization group analysis across different discretization scales.

Contribution

It presents a new holonomy-based approach to operator spin foam models, enabling natural comparison and renormalization across various discretizations.

Findings

Provides a dual holonomy formulation suited for coarse graining.

Defines a renormalization group flow on 2-complexes.

Enables comparison of models at different scales.

Abstract

A dual holonomy version of operator spin foam models is presented, which is particularly adapted to the notion of coarse graining. We discuss how this leads to a natural way of comparing models on different discretization scales, and a notion of renormalization group flow on the partially ordered set of 2-complexes.