Emergent general relativity in fuzzy spaces from tensor models

Details Emergent general relativity in fuzzy spaces from tensor models Emergent general relativity in fuzzy spaces from tensor models

2008-03-12

arxiv.org/abs/0803.1717v3

Prog. Theor. Phys. 119 (2008), 1029

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, 6 figures, a paragraph on effective action added in Conclusion, and other minor changes. A reference added

Scientific paper

10.1143/PTP.119.1029

Tensor models can be regarded as theories of dynamical fuzzy spaces, and provide background independent theories of space. Their classical solutions correspond to classical background spaces, and the small fluctuations around them can be regarded as fluctuations of fields on them. In this paper, I numerically study a tensor model around its classical backgrounds of two-, three- and four-dimensional fuzzy flat tori and show that the properties of low-lying low-momentum modes are in clear agreement with general relativity. Numerical analysis also suggests that the lowest-order effective action is composed of curvature square terms, which is consistent with general relativity in view of the form of the considered action of the tensor model.

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