The perturbative Regge-calculus regime of Loop Quantum Gravity

TL;DR

This paper demonstrates that a semiclassical regime of Loop Quantum Gravity can be effectively described by perturbative area-Regge-calculus, with explicit correlation functions matching between the two frameworks.

Contribution

It establishes a concrete link between Loop Quantum Gravity and perturbative Regge calculus in a specific semiclassical regime, providing explicit correlation function comparisons.

Findings

Correlation functions match between Loop Quantum Gravity and Regge calculus

Identifies a semiclassical regime with large spins and superpositions of four-valent spin networks

Shows the effective description is valid for a single 4-simplex geometry

Abstract

The relation between Loop Quantum Gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the Barrett-Crane vertex amplitude is known to be related to the Regge action. In this paper we study a semiclassical regime of Loop Quantum Gravity and show that it admits an effective description in terms of perturbative area-Regge-calculus. The regime of interest is identified by a class of states given by superpositions of four-valent spin networks, peaked on large spins. As a probe of the dynamics in this regime, we compute explicitly two- and three-area correlation functions at the vertex amplitude level. We find that they match with the ones computed perturbatively in area-Regge-calculus with a single 4-simplex, once a specific perturbative action and measure have been chosen in the Regge-calculus path integral. Correlations of other geometric operators and the existence of this regime for other models for the dynamics are briefly discussed.