Group field theory on 2-groups

TL;DR

This paper introduces a new group field theory based on 2-groups (crossed modules) that generates four-dimensional topological models, linking Feynman diagram amplitudes with Pachner moves and potentially serving as a dual to the Yetter-Mackaay model.

Contribution

It develops a novel group field theory on 2-groups that produces four-dimensional topological invariants, expanding the framework for quantum gravity models.

Findings

Feynman diagram amplitudes relate to Pachner moves

Model is likely dual to the Yetter-Mackaay model

Provides a new approach to 4D topological quantum field theories

Abstract

Group field theories are quantum field theories built on groups. They can be seen as a tool to generate topological state-sums or quantum gravity models. For four dimensional manifolds, different arguments have pointed towards 2-groups (such as crossed modules) as the relevant symmetry structure to probe four dimensional topological features. Here, we introduce a group field theory built on crossed modules which generate a four dimensional topological model, as we prove that the Feynman diagram amplitudes can be related by Pachner moves. This model is presumably the dual version of the Yetter-Mackaay model.