Einstein-Regge equations in spinfoams

TL;DR

This paper demonstrates that spinfoam quantum gravity models, under a specific double scaling limit, reproduce Einstein's equations and reveal quantum and discreteness corrections to classical gravity.

Contribution

It shows that in a particular limit, spinfoam amplitudes become Regge-like path integrals enforcing Einstein equations, including new corrections from geometric discreteness.

Findings

Spinfoam amplitudes reduce to Regge-like path integrals.

Einstein equations emerge in the semiclassical limit.

Discreteness of spectra introduces new quantum corrections.

Abstract

We consider spinfoam quantum gravity on a spacetime decomposition with many 4-simplices, in the double scaling limit in which the Immirzi parameter $\gamma$ is sent to zero (flipped limit) and the physical area in Planck units ($\gamma$ times the spin quantum number $j$) is kept constant. We show that the quantum amplitude takes the form of a Regge-like path integral and enforces Einstein equations in the semiclassical regime. In addition to quantum corrections which vanish when the Planck constant goes to zero, we find new corrections due to the discreteness of geometric spectra which is controlled by the Immirzi parameter.