Abstract
The tensor model is discussed as theory of dynamical fuzzy spaces and as a way to formulate gravity on fuzzy spaces. From numerical analyses, it is shown that the low‐lying long‐wavelength fluctuation spectra around Gaussian background solutions in the tensor model are in agreement with the geometric fluctuations on flat spaces in the general relativity. It is also shown that part of the orthogonal symmetry of the tensor model spontaneously broken by the backgrounds correspond to the local translation symmetry of the general relativity. Thus the tensor model can provide an interesting model of simultaneous emergence of space and the general relativity including the local translation symmetry.
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