Regge gravity from spinfoams

TL;DR

This paper demonstrates how spinfoam quantum gravity approaches can recover Regge calculus and Einstein equations in a specific classical limit, revealing quantum corrections and potential running of the Barbero-Immirzi parameter.

Contribution

It shows that in a combined classical and flipped limit, spinfoam models effectively become Regge-like theories with geometries satisfying Einstein equations.

Findings

Spinfoam models reduce to Regge calculus in the classical limit.

Quantum corrections are characterized by powers of $l_P^2/a$ and $\gamma l_P^2/a$.

Barbero-Immirzi parameter may decrease under coarse-graining.

Abstract

We consider spinfoam quantum gravity for general triangulations in the regime $l_P^2\ll a\ll a/\gamma$, namely in the combined classical limit of large areas $a$ and flipped limit of small Barbero-Immirzi parameter $\gamma$, where $l_P$ is the Planck length. Under few working hypotheses we find that the flipped limit enforces the constraints that turn the spinfoam theory into an effective Regge-like quantum theory with lengths as variables, while the classical limit selects among the possible geometries the ones satisfying the Einstein equations. Two kinds of quantum corrections appear in terms of powers of $l^2_P/a$ and $\gamma l_P^2/a$. The result also suggests that the Barbero-Immirzi parameter may run to smaller values under coarse-graining of the triangulation.