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Fractal Dimension in 3d Spin-Foams · Around

2009

Fractal Dimension in 3d Spin-Foams

Caravelli, Francesco, Modesto, Leonardo

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In this paper we perform the calculation of the spectral dimension of the space-time in 3d quantum gravity using the dynamics of the Ponzano-Regge vertex (PR) and its quantum group generalization (Turaev-Viro model (TV)).

We realize this considering a very simple decomposition of the 3d space-time and introducing a boundary state which selects a classical geometry on the boundary.
We obtain that the spectral dimension of the space-time runs from 2 to 3, across a 1.5 phase, when the energy of a probe scalar field decreases from high to low energy.
For the TV model the spectral dimension at hight energy increase with the value of the cosmological constant.

Built on

V. G. Turaev, O. Y. Viro: State sum invariants of 3-manifolds and quantum 6j-symbols. Topology 31, 865–902 (1992)
1992
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D. D. Reid, The Manifold dimension of a causal set: Tests in conformally flat space-times
Original
2003
Earlier work this paper cites.
C. Rovelli, Graviton propagator from background-independent quantum gravity
2003
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C. Rovelli, Quantum Gravity
2004
Earlier work this paper cites.
D. ben-Avraham and S. Havlin, Diffusion and reactions in fractals and disordered systems
2004
Earlier work this paper cites.

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