Convergence of Loll's CDT and Assymptotic Safety.

[MTd2]

Loll's CDT and Assymptotic Safety proven to be directly related.

The interesting part is this one:

7. Lattice
Lattice implementations for gravity in four dimensions have been put forward based on Regge
calculus techniques [27, 28] and causal dynamical triangulations [29]. [...]

Within the causal dynamical triangulation approach, global aspects of quantum space-times
have been assessed in [29].[...] The key result is that the measured effective dimensionality displays a cross-overfrom d ≈ 4 at large scales to d ≈ 2 at small scales of the order of the Planck scale. This behaviourcompares nicely with the cross-over of the graviton anomalous dimension h under the renormalisationgroup (see Sec. 2), and with renormalisation group studies of the spectral dimension (see
[3, 4, 60]). These findings corroborate the claim that asymptotically safe quantum gravity behaves, in an essential way, two-dimensional at short distances.

http://arxiv.org/abs/0810.3675

I don't know Assymptotic Safety, but now, I really feel motivated to study this since it seems to be an effective bridge between the micro CDT world and our macroscopic world.

:rofl: That's A HUGE FINDING! Great!

PS.: It seems that the Lattice approach is the right one!

 

[marcus]

Some extra information: Daniel Litim, the author of the paper you mention (a talk he gave at the Trieste conference in summer 2007) afterwards organized a 5-day school/workshop which took place in September 2008 and brought together CDT people (Loll, Ambjorn, Jurkiewicz,...) with Asym. Saf. people (Reuter, Percacci, Rahmede, Niedermaier, Bonanno...).

2-day school (to initiate new PdD students)
http://www.ippp.dur.ac.uk/Workshops/08/NPMQFT
3-day workshop (current research)
http://www.ippp.dur.ac.uk/Workshops/08/CLAQG

The slides of the workshop talks are available online. The scope of the workshop was wider than just the two approaches of Loll or Reuter and their friends. But by my count the two largest contingents at the workshop were those: the CDT people and the Asym. Safety people.

By the way he structured the workshop (and the introductory school preceding it) Daniel Litim seems to me to have defined a convergence and a direction. He did this in an interesting way, I think. I also think it was more or less in line with what you are saying.

The fact that both approaches independently arrived at lower dimensionality at small scale could, I agree, be quiite exciting.

 

[MTd2]

The fact that both approaches independently arrived at lower dimensionality at small scale could, I agree, be quiite exciting.

Which is the same dimensionality of all string theories, including the non-critical, which is where CDT started and came from. So, we see that the 2-dimensional thing is really important, more than strings, CDT or anything else.

Hmm, independently of, I think a figured out an intuition to look for a path to naturaly emerge QM out of certain kinds of 4-manifolds. And these are related to 2-d structures. It's not something that I invented, I just noticed one of these days when reading some geometry... But I really don't know if anyone would care and, instead, called me crazy or crackpot

 

[marcus]

I have a general attitude about this which is that at this stage what we are seeing (with Loll, Reuter, Benedetti, perhaps perhaps even some geometer like Hendrik Pfeifer...) is a fluid picture that is gradually solidifying or coming into focus.

The basic intuition should only be to recognize that it could be important, not to seize on some one particular idea and think this is the right way to look at it. That's my attitude about this now.

I only recognize that it might be important that two 4D continuums have appeared that both are familiar 4D smooth at macro scale but the spectral dimensionality declines continuously down to around 2D as you zoom into micro scale. The graph looks like it takes a "nose-dive" at near Planck scale.

And now Benedetti has found that this diving scale-dependent dimensionality is just what should be expected from a noncommutative spacetime with quantum group symmetry. Indeed you spotted the Benedetti paper last week and were very excited by it, as I recall. (I was too.)

http://arxiv.org/abs/0811.1396
Fractal properties of quantum spacetime
D. Benedetti

"We show that in general a spacetime having a quantum group symmetry has also a scale-dependent fractal dimension..."

Now this makes the intuitive case even stronger. Maybe some people already see a clear signpost pointing what direction things will go. I don't. I see only that it is interesting and potentially important. I notice some things like
1. a quantum group is not a group, it is a kind of noncommutative algebra
2. a Loll continuum is not (I think) a differential manifold
3. usual-type manifolds are smooth down to micro scale and these new continuums seem to be chaotic at small scale---chaos appears as you zoom in

Mathematically unfamiliar things are appearing here. So I am doubtful that anybody is able to have the right idea at this point---maybe differential manifold is not even the right model of the continuum. Prevalent ideas such as superstring may turn out to be constructed on the wrong basic premise---if they are built on differential geometry with the fundamental objects being differential manifolds of whatever classical integer dimensionality.

However this is just my point of view, and I don't insist that anyone else share it. If you see what is coming out of this situation, then maybe you should work on it. Maybe your guess could turn out to be right.