Emergent Geometry from Quantized Spacetime

Hyun Seok Yang; M. Sivakumar

doi:10.1103/physrevd.82.045004

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arXiv · 0908.2809

Emergent Geometry from Quantized Spacetime

Hyun Seok Yang·M. Sivakumar

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Abstract

We examine the picture of emergent geometry arising from a mass-deformed matrix model. Because of the mass-deformation, a vacuum geometry turns out to be a constant curvature spacetime such as d-dimensional sphere and (anti-)de Sitter spaces. We show that the mass-deformed matrix model giving rise to the constant curvature spacetime can be derived from the d-dimensional Snyder algebra. The emergent geometry beautifully confirms all the rationale inferred from the algebraic point of view that the d-dimensional Snyder algebra is equivalent to the Lorentz algebra in (d+1)-dimensional {\it flat} spacetime. For example, a vacuum geometry of the mass-deformed matrix model is completely described by a G-invariant metric of coset manifolds G/H defined by the Snyder algebra. We also discuss a nonlinear deformation of the Snyder algebra.

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Hyun Seok Yang, M. Sivakumar. 2010-08-05. Emergent Geometry from Quantized Spacetime. https://doi.org/10.1103/physrevd.82.045004

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