Emergent four-dimensional linearized gravity from a spin foam model

Abstract

Spin Foam Models (SFMs) are covariant formulations of Loop Quantum Gravity (LQG) in 4 dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries satisfying Einstein equation can emerge from discrete SFMs under an appropriate low energy limit, which corresponds to a semiclassical continuum limit of SFMs. In particular, we show that the low energy excitations of SFMs on a flat background give all smooth solutions of linearized Einstein equations (spin-2 gravitons). This indicates that at the linearized level, classical Einstein gravity is indeed the low energy effective theory from SFMs. Thus our result heightens the confidence that covariant LQG is a consistent theory of quantum gravity. As a key technical tool, a regularization/deformation of the SFM is employed in the derivation. The deformation parameter δ becomes a coupling constant of a higher curvature correction term to Einstein gravity from SFM.

Effective dynamics from coherent state path integral of full loop quantum gravity

“…However the continuum limit requires to take non-perturbative quantum corrections into consideration, and is beyond the scope of this paper (see some recent work e.g. [54][55][56][57] on the continuum limit in LQG). We propose that theμ-scheme should relate to the quantum effective EOM, which may be derived from the quantum effective action of our path integral.…”

Semiclassical behavior of spinfoam amplitude with small spins and entanglement entropy

“…Critical points of S 0 has been completely classified in case that all tetrahedra reconstructed from the closure condition are nondegenerate. We refer the reader to [12,20,28,34] for details of the classification. When J ∆ are areas relating to edge-lengths on K s by ( i j , jk , ik are 3 edge-lengths of a triangle ∆)…”

“…for all v ⊂ K s and all 4 α 1 , α 2 , α 3 , α 4 out of 5 α's at v. We have the following 1-to-1 correspondence [12,34]:…”

“…We denote these critical points by (g ± vα , ξ α∆ ) c [J ∆ ]. Some of these critical points relate to Regge geometries in 4 dimensions similar to the simplicial EPRL-FK amplitude [12,20]. At these critical points, J ∆ is identified to be the area of the triangle ∆.…”

“…The recent progresses on the semiclassical analysis reveal that spinfoam amplitudes relate to the semiclassical Einstein gravity in the large spin regime, e.g. [6][7][8][9][10][11][12][13].…”