Emergent general relativity in fuzzy spaces from tensor models

TL;DR

This paper demonstrates that tensor models can produce fuzzy spaces whose low-energy fluctuations replicate general relativity, suggesting a promising approach to background-independent quantum gravity.

Contribution

It provides numerical evidence that tensor models' classical solutions correspond to fuzzy spaces with properties matching general relativity.

Findings

Low-lying modes agree with general relativity

Effective action includes curvature squared terms

Classical backgrounds are fuzzy flat tori

Abstract

Tensor models can be regarded as theories of dynamical fuzzy spaces, and provide background independent theories of space. Their classical solutions correspond to classical background spaces, and the small fluctuations around them can be regarded as fluctuations of fields on them. In this paper, I numerically study a tensor model around its classical backgrounds of two-, three- and four-dimensional fuzzy flat tori and show that the properties of low-lying low-momentum modes are in clear agreement with general relativity. Numerical analysis also suggests that the lowest-order effective action is composed of curvature square terms, which is consistent with general relativity in view of the form of the considered action of the tensor model.