From Dimensional Reduction of 4d Spin Foam Model to Adding Non-Gravitational Fields to 3d Spin Foam Model

TL;DR

This paper introduces a method to derive non-gravitational matter fields and additional dimensions from a 4d spin foam model using a Kaluza-Klein-like approach, connecting 4d quantum gravity to 3d matter interactions.

Contribution

It presents a novel approach to generate matter fields and extra dimensions from pure 4d quantum gravity models via group field theory and spin foam techniques.

Findings

Reconstruction of matter fields from 4d spin foam models.

Generation of 3d space-time geometry from 4d quantum gravity.

Mechanism for matter emergence and dimensional extension.

Abstract

A Kaluza-Klein like approach for a 4d spin foam model is considered. By applying this approach to a model based on group field theory in 4d (TOCY model), and using the Peter-Weyl expansion of the gravitational field, reconstruction of new non gravitational fields and interactions in the action are found. The perturbative expansion of the partition function produces graphs colored with su(2) algebraic data, from which one can reconstruct a 3d simplicial complex representing space-time and its geometry; (like in the Ponzano-Regge formulation of pure 3d quantum gravity), as well as the Feynman graph for typical matter fields. Thus a mechanism for generation of matter and construction of new dimensions are found from pure gravity.