Emergent general relativity in the tensor models possessing Gaussian classical solutions

TL;DR

This paper reviews how certain tensor models with Gaussian solutions can give rise to emergent general relativity, space, and gauge symmetries through classical solutions and fluctuations.

Contribution

It demonstrates that tensor models with Gaussian backgrounds can reproduce geometric fluctuations and local translation symmetry of general relativity.

Findings

Low-lying fluctuations match geometric fluctuations in GR.

Spontaneous symmetry breaking relates to local translation symmetry.

Tensor models can generate space and gauge symmetries emergently.

Abstract

This paper gives a summary of the author's works concerning the emergent general relativity in a particular class of tensor models, which possess Gaussian classical solutions. In general, a classical solution in a tensor model may be physically regarded as a background space, and small fluctuations about the solution as emergent fields on the space. The numerical analyses of the tensor models possessing Gaussian classical background solutions have shown that the low-lying long-wavelength fluctuations around the backgrounds are in one-to-one correspondence with the geometric fluctuations on flat spaces in the general relativity. It has also been shown that part of the orthogonal symmetry of the tensor model spontaneously broken by the backgrounds can be identified with the local translation symmetry of the general relativity. Thus the tensor model provides an interesting model of simultaneous emergence of space, the general relativity, and its local gauge symmetry of translation.