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Random holographic "large worlds" with emergent dimensions.

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This study introduces a random network model for emergent quantum spacetime, where discrete space is fundamental. The model reveals spontaneous emergence of higher dimensions, including time, and demonstrates a holographic principle in its fundamental degrees of freedom.

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • Network Theory

Background:

  • Current models often treat discrete space as a regularization.
  • Understanding emergent spacetime and causality is a key challenge in quantum gravity.

Purpose of the Study:

  • To propose a novel random network model for emergent quantum spacetime.
  • To investigate the emergence of spacetime dimensions and causality from fundamental principles.
  • To explore the holographic principle within this discrete framework.

Main Methods:

  • Utilizing a random network model with Gaussian weights and Ising link antiferromagnetism.
  • Analyzing spectral and Hausdorff dimensions of quenched graphs.
  • Investigating emergent causality in the large N limit.

Main Results:

  • Discrete space is fundamental, with spectral dimension determined by coupling constant.
  • Spontaneous emergence of embedding spaces with Hausdorff dimensions 4 and 5 for d_s=2 and d_s=3.
  • Emergent time and causality in the large N limit.
  • Demonstration of a holographic principle with degrees of freedom scaling as N^(2/5).

Conclusions:

  • The proposed model offers a new perspective on quantum spacetime emergence.
  • The model naturally incorporates discrete geometry, emergent dimensions, and causality.
  • It provides a graph-theoretic realization of the holographic principle.