#### MTd2

Gold Member

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Dear Petr Horava,

In your article you say that your result reproduces the lattice computations of

J. Ambjørn, J. Jurkiewicz, and R. Loll, Spectral Dimension of the Universe, Phys. Rev. Lett. 95

(2005) 171301, [hep-th/0505113].

but I'd like to know if you are aware that these computations that reproduces this result were already reproduced by:

Leonardo Modesto, "Fractal Structure of Loop Quantum Gravity", http://arxiv.org/abs/0812.2214

Which tries to find a link between LQG, CDT and assymptotic safety. Check page. 3, section "4d space time", equations 22 and 23 and the plot on figure 4, page.4. This is based on the results of one of the collaborator of Renate Loll research group:

Dario Benedetti, "Fractal properties of quantum spacetime", http://arxiv.org/abs/0811.1396

Given the similar claims and that the fits to the lattice computatons of the spectral dimension are also very recent, I thought your paper would have some comments concening the above articles.

Just a random question. A few years ago, I saw some sugestions from Ashok Sen and Sergei Gukov that LQG could be a low limit energy of a M-Theory. I am aware of the negative probability states that plague LQG and also the problem with identifying the Plebanski actions with the lagragians that are used in LQG. But given the converging results in these plots, do you think that by imposing some restrictions on LQG, one can obtain LQG as a limit of m theory.

Eyo Eyo Ita is a guy that works with anisyotropic space time as a restriction to LQG like theories. This Ita's articles:

http://arxiv.org/find/all/1/all:+AND+ita+AND+eyo+eyo/0/1/0/all/0/1

I guess most of his recent articles are relevant to the discussions, even since he tries to fix the negative Kodama states by an anisyotropic space restriction.

Cheers,

Daniel.