Modified Graviton Dynamics From Spin Foams: The Area Regge Action

TL;DR

This paper investigates the dynamics of the Area Regge action in 4D quantum gravity, revealing that on a hyper-cubical lattice, it naturally leads to the Length Regge action through its scaling behavior, without explicit constraints.

Contribution

First systematic analysis of Area Regge dynamics on a hyper-cubical lattice showing it converges to Length Regge action via scaling behavior.

Findings

Linearized Area Regge action singles out Length Regge action.

Scaling behavior in lattice constant emerges without explicit constraints.

Higher order terms in lattice constant are identified.

Abstract

A number of approaches to 4D quantum gravity, such as holography and loop quantum gravity, propose areas instead of lengths as fundamental variables. The Area Regge action, which can be defined for general 4D triangulations, is a natural choice for an action based on areas. It does indeed appear in the semi-classical limit of spin foam models. The Area Regge action does however only lead to a discrete version of the gravitational equations of motion, if one implements constraints, that ensure that the areas are compatible with a consistent length assignment to the edges of the triangulation. The constrained version is then classically equivalent to the Length Regge action, which provides a discretization of the Einstein-Hilbert action. Here we perform the first systematic analysis of the Area Regge dynamics on a hyper-cubical lattice. Surprisingly, we find that the linearized Area Regge action on a hyper-cubical lattice does single out the Length Regge action by its scaling behaviour in the lattice constant. That is, integrating out the variables describing fluctuations in the area-length constraints one finds the linearized Length Regge action plus terms of higher order in the lattice constant. This appears without any explicit implementation of the area-length constraints.