Tensor Models as Theory of Dynamical Fuzzy Spaces and General Relativity

Abstract

The tensor model is discussed as theory of dynamical fuzzy spaces in order to formulate gravity on fuzzy spaces. The numerical analyses of the tensor models possessing Gaussian background solutions have shown that the low‐lying long‐wavelength fluctuations around the backgrounds are in remarkable agreement 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 agrees 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 translation symmetry.