A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity

TL;DR

This paper introduces a new class of Group Field Theory models that unify loop quantum gravity and simplicial quantum gravity by providing path integral formulations of discrete gravity actions across various dimensions.

Contribution

The paper constructs a novel class of GFT models with Feynman amplitudes corresponding to discrete gravity actions in 1st order variables, applicable to any spacetime dimension and signature.

Findings

Models reproduce 1st order Regge calculus in 3D

Models generalize to higher dimensions with discrete BF theory

Insights into semi-classical limits of spin foam models

Abstract

Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any choice of spacetime dimension and signature, whose Feynman amplitudes are given by path integrals for clearly identified discrete gravity actions, in 1st order variables. In the 3-dimensional case, the corresponding discrete action is that of 1st order Regge calculus for gravity (generalized to include higher order corrections), while in higher dimensions, they correspond to a discrete BF theory (again, generalized to higher order) with an imposed orientation restriction on hinge volumes, similar to that characterizing discrete gravity. The new models shed also light on the large distance or semi-classical approximation of spin foam models. This new class of group field theories may represent a concrete unifying framework for loop quantum gravity and simplicial quantum gravity approaches.