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

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.

29 pages, 13 figures

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• Tensor models and hierarchy of n-ary algebras
• Gauge fixing in the tensor model and emergence of local gauge symmetries
• The lowest modes around Gaussian solutions of tensor models and the general relativity
• Tensor models and 3-ary algebras
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• A renormalization procedure for tensor models and scalar-tensor theories of gravity
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