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DOE OSTI · 21420991

Emergent geometry from quantized spacetime

Yang, Hyun Seok·Sivakumar, M
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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 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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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDSANTI DE SITTER SPACEDEFORMATIONMANY-DIMENSIONAL CALCULATIONSMASSMATHEMATICAL SPACEMETRICSNONLINEAR PROBLEMSSIMULATIONSPACESPACE-TIME

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Yang, Hyun Seok, Sivakumar, M. 2010-08-15. Emergent geometry from quantized spacetime. https://doi.org/10.1103/physrevd.82.045004

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