Tensor Models as Theory of Dynamical Fuzzy Spaces and General Relativity

Journal Article · Thu Jun 17 00:00:00 EDT 2010 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3460182· OSTI ID:21366967

Sasakura, Naoki ^[1]

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1. Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa, Sakyo-ku, Kyoto 606-8502 (Japan)

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.

• OSTI ID: 21366967
• Journal Information: AIP Conference Proceedings, Vol. 1243, Issue 1; Conference: 8. international workshop on Lie theory and its applications in physics, Varna (Bulgaria), 15-21 Jun 2009; Other Information: DOI: 10.1063/1.3460182; (c) 2010 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
FUZZY LOGIC
GENERAL RELATIVITY THEORY
GEOMETRY
GRAVITATION
LIE GROUPS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
NUMERICAL ANALYSIS
SYMMETRY
SYMMETRY BREAKING
TENSORS
WAVELENGTHS
FIELD THEORIES
MATHEMATICAL LOGIC
MATHEMATICS
RELATIVITY THEORY
SPACE
SYMMETRY GROUPS