Coupling of spacetime atoms and spin foam renormalisation from group field theory

TL;DR

This paper introduces a generalized spin foam model from group field theory that incorporates coupling between 4-simplices, allowing for tunable locality and offering insights into renormalisation processes.

Contribution

It develops a new coupled spin foam model with a tunable parameter and extends the group field theory formalism to include this coupling, aiding renormalisation analysis.

Findings

The model interpolates between Barrett-Crane and BF-type models.

The coupling parameter can be tuned to adjust locality.

The extended formalism facilitates renormalisation studies.

Abstract

We study the issue of coupling among 4-simplices in the context of spin foam models obtained from a group field theory formalism. We construct a generalisation of the Barrett-Crane model in which an additional coupling between the normals to tetrahedra, as defined in different 4-simplices that share them, is present. This is realised through an extension of the usual field over the group manifold to a five argument one. We define a specific model in which this coupling is parametrised by an additional real parameter that allows to tune the degree of locality of the resulting model, interpolating between the usual Barrett-Crane model and a flat BF-type one. Moreover, we define a further extension of the group field theory formalism in which the coupling parameter enters as a new variable of the field, and the action presents derivative terms that lead to modified classical equations of motion. Finally, we discuss the issue of renormalisation of spin foam models, and how the new coupled model can be of help regarding this.