Emergent general relativity in the tensor models possessing Gaussian classical solutions

Abstract

This paper gives a summary of the author's works concerning the emergent general relativity in a particular class of tensor models, which possess Gaussian classical solutions. In general, a classical solution in a tensor model may be physically regarded as a background space, and small fluctuations about the solution as emergent fields on the space. The numerical analyses of the tensor models possessing Gaussian classical background solutions have shown that the low-lying long-wavelength fluctuations around the backgrounds are in one-to-one correspondence 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 can be identified 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 gauge symmetry of translation.

15pages, 5 figures, based on the proceedings of VIII International Workshop, "Lie Theory and its Applications in Physics", Varna, 15 - 21 June 2009, and of XXV Max Born Symposium, ``The Planck Scale'', Wroclaw, 29 June - 3 July 2009

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• Tensor model and dynamical generation of commutative nonassociative fuzzy spaces
• 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
• The fluctuation spectra around a Gaussian classical solution of a tensor model and the general relativity

Cited by in corpus (3)

• Canonical tensor models with local time
• Super tensor models, super fuzzy spaces and super n-ary transformations
• Tensor models and 3-ary algebras