Quantum Gravity via Random Triangulations of R^4 and Gravitons as Goldstone Bosons of SL(4)/O(4)

TL;DR

This paper proposes a model of random triangulations in four-dimensional space, suggesting that spontaneous symmetry breaking of SL(4) to O(4) could lead to a continuum limit of quantum gravity with massless gravitons as Goldstone bosons.

Contribution

It introduces a novel random triangulation model with SL(4) symmetry and explores its phase structure, proposing a mechanism for emergent quantum gravity.

Findings

SL(4) symmetry is spontaneously broken to O(4) in a stable phase.

Correlation length in the spin two channel is infinite in the broken phase.

Potential continuum limit of 4D quantum gravity identified within the model.

Abstract

A model of random triangulations of a domain in $R^{(4)}$ is presented. The global symmetries of the model include SL(4) transformations and translations. If a stable microscopic scale exists for some range of parameters, the model should be in a translation invariant phase where SL(4) is spontaneously broken to O(4). In that phase, SL(4) Ward identities imply that the correlation length in the spin two channel of a symmetric tensor field is infinite. Consequently, it may be possible to identify the continuum limit of four dimensional Quantum Gravity with points inside that phase.