The fluctuation spectra around a Gaussian classical solution of a tensor model and the general relativity

TL;DR

This paper numerically analyzes fluctuation spectra around a Gaussian solution in a tensor model, finding results consistent with general relativity's metric tensor behavior in multiple dimensions, supporting the model's relevance to emergent gravity.

Contribution

It demonstrates that the fluctuation spectra of a tensor model align with general relativity, suggesting the model can describe emergent gravitational dynamics.

Findings

Low-lying spectra match metric tensor distributions in general relativity.

Results are consistent across one to four dimensions.

Supports tensor models as a framework for emergent gravity.

Abstract

Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this paper, I study numerically the fluctuation spectra around a Gaussian classical solution of a tensor model, which represents a fuzzy flat space in arbitrary dimensions. It is found that the momentum distribution of the low-lying low-momentum spectra is in agreement with that of the metric tensor modulo the general coordinate transformation in the general relativity at least in the dimensions studied numerically, i.e. one to four dimensions. This result suggests that the effective field theory around the solution is described in a similar manner as the general relativity.