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

Emergent general relativity in the tensor models possessing Gaussian classical solutions