3nj-symbols and D-dimensional quantum gravity

TL;DR

This paper explores a generalized model of Euclidean quantum gravity in D dimensions, linking the Einstein-Regge action for a D-simplex to Gaussian integrals of 3nj-symbols, extending previous 3D and 4D models.

Contribution

It introduces a unified framework connecting D-dimensional Euclidean quantum gravity with 3nj-symbols, generalizing prior 3D and 4D models to higher dimensions.

Findings

Establishes a semiclassical limit expression for the Einstein-Regge action using 3nj-symbols.

Generalizes the Ponzano-Regge and Carfora-Martellini-Marzuoli models to arbitrary dimensions.

Provides a mathematical foundation for D-dimensional quantum gravity models.

Abstract

The model which generalizes Ponzano and Regge $3D$ and Carfora-Martellini-Marzuoli $4D$ euclidean quantum gravity is considered. The euclidean Einstein-Regge action for a $D$-simplex is given in the semiclassical limit by a gaussian integral of a suitable $3nj$-symbol.