Emergent Geometry from Quantized Spacetime

Details Emergent Geometry from Quantized Spacetime Emergent Geometry from Quantized Spacetime

2009-08-20

arxiv.org/abs/0908.2809v4

Phys. Rev. D82 (2010) 045004

Physics

High Energy Physics

High Energy Physics - Theory

33 pages; Published version in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.82.045004

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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