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Are asymptotic safety and causal dynamical triangulation compatible? https://arxiv.org/pdf/1411.7712.pdf As you all know AS has problems with the holographic principle. However, the dimensional reduction obtained in asymptotic safety by using causal dynamical triangulation can make AS compatible with the holographic principle. So, are AS and CDT different parts of the same theory? Are they compatible? If so, then how? Asymptotic safety is linear with respect to the wave function, while causal dynamical triangulation is non-linear. If these two where to merge, would the final theory be linear or non linear?

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    $\begingroup$ Minor comment to the post (v1): In the future please link to abstract pages rather than pdf files, e.g., arxiv.org/abs/1411.7712 $\endgroup$ – Qmechanic Apr 25 '17 at 20:35
  • $\begingroup$ @Qmechanic what do you mean? $\endgroup$ – Jag Apr 25 '17 at 22:09
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I don't know exactly what you mean but I can summarize what this paper says. If gravity is asymptotically safe, then one expects a fixed point in the UV (small scales) around which the theory is conformal field theory (CFT). For a CFT, one expects that entropy will go as, $\sim S ∼ E^{(d-1)/d}$ [See https://arxiv.org/abs/0709.3555]. In GR, the entropy goes as, $\sim S ∼ E^{(d-2)/(d-3)}$. They are clearly not the same for d=4. The author then notes - "It therefore follows that the large energy asymptotics of the density of states in a theory of gravity in asymptotically flat spacetime is not that of any conformal field theory, and therefore, it is not a renormalizable quantum field theory".

The paper you mention argues that the geometry of our four dimensional space-time in the UV has a different dimension, which is d=3/2. If d=3/2, then the scaling of entropies mentioned above agrees and hence - gravity can still be asymptotically safe.

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