12j-symbols and four-dimensional quantum gravity

TL;DR

This paper introduces a model for four-dimensional Euclidean quantum gravity that connects the exponential of the Einstein-Regge action to a gaussian integral of a 12j-symbol, extending previous 3D models.

Contribution

It presents a novel four-dimensional quantum gravity model linking the Einstein-Regge action to 12j-symbols, generalizing the 3D Ponzano-Regge model.

Findings

In the semiclassical limit, the 12j-symbol approximates the exponential of the Einstein-Regge action.

The model provides a new mathematical framework for 4D quantum gravity.

Discussion of potential developments and implications of this approach.

Abstract

We propose a model which represents a four-dimensional version of Ponzano and Regge's three-dimensional euclidean quantum gravity. In particular we show that the exponential of the euclidean Einstein-Regge action for a $4d$-discretized block is given, in the semiclassical limit, by a gaussian integral of a suitable $12j$-symbol. Possible developments of this result are discussed.