Wednesday, July 24, 2013

1307.6122 (Michele Arzano et al.)

Black-hole entropy and minimal diffusion    [PDF]

Michele Arzano, Gianluca Calcagni
The density of states reproducing the Bekenstein-Hawking entropy-area scaling can be modelled via a nonlocal field theory. We define a diffusion process based on the kinematics of this theory and find a spectral dimension whose flow exhibits surprising properties. While it asymptotes the infrared value of four from above, in the ultraviolet the spectral dimension diverges at a finite (Planckian) value of the diffusion length, signalling a breakdown of the notion of diffusion on a continuum spacetime below that scale. The correlation length remains finite throughout the flow. We comment on the implications of this minimal diffusion scale for the entropy bound in a holographic and field-theoretic context.
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