Group field theory and simplicial quantum gravity

TL;DR

This paper introduces a new 4D Group Field Theory for quantum gravity that explicitly encodes simplicial path integrals, linking it directly to other approaches like Regge calculus and dynamical triangulations.

Contribution

It develops a novel GFT model that incorporates gravity constraints and provides a clear geometric interpretation, bridging various simplicial quantum gravity methods.

Findings

Quantum amplitudes match simplicial path integrals for 1st order gravity

The model's variables have a clear geometric interpretation

Connections to quantum Regge calculus and dynamical triangulations are established

Abstract

We present a new Group Field Theory for 4d quantum gravity. It incorporates the constraints that give gravity from BF theory, and has quantum amplitudes with the explicit form of simplicial path integrals for 1st order gravity. The geometric interpretation of the variables and of the contributions to the quantum amplitudes is manifest. This allows a direct link with other simplicial gravity approaches, like quantum Regge calculus, in the form of the amplitudes of the model, and dynamical triangulations, which we show to correspond to a simple restriction of the same.