The Emergence of Gravity: The Case for a New Theory of Spacetime Structure

[atyy]

In a recent thread, marcus brought my attention to 't Hooft's Quantum gravity without space-time singularities or horizons http://arxiv.org/abs/0909.3426 .

For emergent gravity, the major no-go theorem is the Weinberg-Witten theorem, which string theory gets round apparently by having space emerge with gravity. In a footnote of their paper, Weinberg and Witten state "The theorem does not apply to theories in which the gravitational field is a basic degree of freedom, but the Einstein action is induced by quantum effects" (Is this why Wen has been making cryptic remarks about long range entanglement?) They go on to list a bunch of theories which aren't excluded by their theorem, which includes, in addition to Sakharov's original induced gravity and many others:

Towards a theory of spacetime structure at very short distances
Lee Smolin
Nuclear Physics B 160: 253-268, 1979
Renormalization-group arguments are summarized which suggest that at distances shorter than the Planck length the spacetime geometry should be asymptotically scale invariant. A new locally scale-invariant extension of general relativity is then proposed based on Weyl's conformally invariant geometry. It is shown that if the theory contains a Higgs phase, then it reduces to Einstein's theory in the limit of large distances. Finally, the theory incorporates the non-linear sigma model, which suggests a new approach to the calculation of non-perturbative, short-distance effects in quantum gravity.

OK, I'm free associating here between a paper I don't understand at all ('t Hooft's) and another I haven't read (can't seem to get Smolin's paper free). While I'm at it, let me also bring up Strominger's comment in http://arxiv.org/abs/0906.1313: "If gravity is induced, which means that Newton’s constant is zero at tree level and arises as a one loop correction, then the entanglement entropy is responsible for all of the entropy, and reproduces the area law with the correct coefficient. This might in fact be the case in string theory, where the Einstein action is induced at one loop from open strings, but this notion has yet to be made precise. Recent progress has revealed a rich holographic relation between entanglement entropy and minimal surfaces including horizons."

 

[marcus]

...
Towards a theory of spacetime structure at very short distances
Lee Smolin
Nuclear Physics B 160: 253-268, 1979
Renormalization-group arguments are summarized which suggest that at distances shorter than the Planck length the spacetime geometry should be asymptotically scale invariant. A new locally scale-invariant extension of general relativity is then proposed based on Weyl's conformally invariant geometry. It is shown that if the theory contains a Higgs phase, then it reduces to Einstein's theory in the limit of large distances. Finally, the theory incorporates the non-linear sigma model, which suggests a new approach to the calculation of non-perturbative, short-distance effects in quantum gravity.

(can't seem to get Smolin's paper free).

I looked around and found you a free Japanese scan of the paper:
http://ccdb4fs.kek.jp/cgi-bin/img/allpdf?197909044

This paper is interesting for several reasons. It's dated 1979 the same year Smolin finished his PhD at Harvard and moved to the IAS Princeton.
It cites the two main sources for Asymptotic Safety. Weinberg's 1976 Erice lectures and his chapter in an Einstein Centennial volume edited by Hawking.
And Weinberg in return cites Smolin on Asymptotic Safety. Not this precise paper but a followup on it that Smolin wrote at Princeton soon afterwards.

The paper is interesting not only for its connection with renormalization/asymptotic safety but also with scale invariance---conformal invariance. The sort of thing that as you point out 't Hooft (and also Nicolai) were talking about just recently.

 

[atyy]

I looked around and found you a free Japanese scan of the paper:
http://ccdb4fs.kek.jp/cgi-bin/img/allpdf?197909044

Thanks! Also maybe related:

Anderson http://arxiv.org/abs/gr-qc/9912051 "Therefore one does not need to introduce these ideal clocks and rods and hence has no need of a metric."

Krasnov http://arxiv.org/abs/0812.3603 "While the propagation of light is a very basic process that can arguably make sense to be built into the very definition of the spacetime structure, the availability of rulers and clocks at every point is on a very different footing. ..... Indeed, in Section VII we have seen how a version of “induced gravity” scenario is possible in our setting."

 

[marcus]

...
Towards a theory of spacetime structure at very short distances
Lee Smolin
Nuclear Physics B 160: 253-268, 1979
"Renormalization-group arguments are summarized which suggest that at distances shorter than the Planck length the spacetime geometry should be asymptotically scale invariant. A new locally scale-invariant extension of general relativity is then proposed based on Weyl's conformally invariant geometry. It is shown that if the theory contains a Higgs phase, then it reduces to Einstein's theory in the limit of large distances..."

OK, I'm free associating here between a paper I don't understand at all ('t Hooft's) and another I haven't read (can't seem to get Smolin's paper free). ...

Some of your (free?) associations are, at least by my standards, brilliant. I don't know whether to call them free associations or simply associations--glimpses of suggestive similarity and possible connection. And some associations don't ring a bell for me, so in that case I normally don't respond.

Let's idle down and take a longer look at your O.P. citation---the 1979 Smolin paper.
What he is talking about here bears an uncanny resemblance to what Hermann Nicolai was just asking for in 2009---thirty years later---in his Planck Scale conference talk.

We ought to take some time to patiently mull that over, I think.

 

[marcus]

Smolin was born 1955 and despite being a high school dropout managed to get back into the educational system after a few years and obtained his PhD from Harvard by 1979 at age 24. He wrote two papers about the topic (asymptotic conformal gravity) introduced in this thread.

The first one, written when he was 24, was immediately published by NPB and has been cited 165 times:
Towards a theory of spacetime structure at very short distances
Nuclear Physics B 160: 253-268, 1979

This longer followup paper, written at age 27, was also published by NPB and has so far been cited 39 times, most recently in 2009 by Steven Weinberg:
A Fixed Point For Quantum Gravity.
Published in Nucl.Phys.B208:439,1982.

With that kind of publication/citation record, I can't dismiss this attempt at asymptotic conformal gravity as negligible or crazy. The thing that gets me is the strange overlap (at several points, not just one) with the 2006 idea of Kris Meissner and Hermann Nicolai which they introduced here:
http://arxiv.org/abs/hep-th/0612165

They point out that the Standard Model is almost conformally invariant (scale free) and that its conformal symmetry could be broken in natural way by the C-W mechanism (suggested by Sidney Coleman and Erick Weinberg) if there were a 4D quantum gravity spacetime which was asymptotic conformal, that you could put it on.

Nicolai made that the topic of his Planck Scale 2009 talk, of which the video:
http://www.ift.uni.wroc.pl/~rdurka/planckscale/index-video.php?plik=http://panoramix.ift.uni.wroc.pl/~planckscale/video/Day1/1-3.flv&tytul=1.3%20Nicolai

In case anyone is curious about the recent Steven Weinberg paper, it's here:
http://arxiv.org/abs/0908.1964
You can find Smolin's 1982 paper cited on page 19, reference [36].
Having never been introduced to him, I cannot say whether Steven Weinberg is a gentleman or not, but he is certainly a scholar.
There is an interesting bloodline here. Sidney Coleman, whose name keeps coming up in this context, was Smolin's thesis advisor at Harvard, and definitely a good advisor to have.

Atyy, you also mentioned 't Hooft's 2009 Erice talk, which shows that 't Hooft also has a conformal bee in his bonnet (American alliterative folk-saying for having something on one's mind.)

't Hooft discussed a conformal symmetry across the black hole horizon, a kind of mirror complementarity between looking in and looking out. And another coincidence is that an oddly similar picture was discussed by Leonardo Modesto (former Rovelli postdoc) at the Planck Scale 2009 conference! Reflection from inside to outside across BH horizon. I cannot easily comprehend how much the conformality theme is surfacing these days.
http://arxiv.org/abs/0909.5421

Well, we really should study the Smolin 1979 paper, since it has 165 citations so far and we have the KEK (Kou Ene Ken "high energy research" in Japanese) scan of it. Who knows, maybe it is an historical paper. Thanks for spotting it and starting a thread!

 

[atyy]

Hmmm, Smolin's paper doesn't seem to be about emergent gravity (in my sense of the word) although I came across it via the Weinberg-Witten paper. It's seems essentially about Asymptotic Safety, which posits a UV fixed point for the gravitational field. As I understand it, field theories at a fixed point must be conformally invariant (or at least scale invariant) by definition of a fixed point. So 't Hooft was actually talking about Asymptotic Safety

 

[atyy]

http://arxiv.org/abs/astro-ph/0505266
Alternatives to Dark Matter and Dark Energy
Philip D. Mannheim

http://arxiv.org/abs/astro-ph/0605504
Fourth order Weyl gravity
Eanna E. Flanagan

http://arxiv.org/abs/hep-th/0603131
Spontaneous breaking of conformal invariance in theories of conformally coupled matter and Weyl gravity
A. Edery, Luca Fabbri, M. B. Paranjape

http://arxiv.org/abs/0710.5402
Spontaneous breaking of conformal invariance, solitons and gravitational waves in theories of conformally invariant gravitation
Jihene Bouchami, M. B. Paranjape
"Conformal gravity ... Perturbative calculations indicate that it is asymptotically free and power counting renormalizable (Stelle, PRD, 1973)"

So is conformal gravity asymptotically free, or is it part of the Asymptotic Safety program?

 

[atyy]

Niedermeier and Reuter http://relativity.livingreviews.org/Articles/lrr-2006-5/ : "The unstable manifold of a fixed point is crucial for the construction of a continuum limit. The fixed point itself describes a strictly scale invariant situation."

Riva and Cardy http://arxiv.org/abs/hep-th/0504197 : "Coleman and Jackiw [1] clarified this issue in the case of four space–time dimensions, showing that conformal invariance is not in general guaranteed by the presence of scale invariance."

So does Asymptotic Safety require conformal invariance?

 

[marcus]

Atyy, I've been wondering along the same lines and cannot confidently answer. I've been looking at some of the sources you dug up. Except to say thanks, I don't have much that's useful to say, so tend to just be quiet. It looks like your Riva and Cardy find will help. I'll take a look at that now.

=================
EDIT TO REPLY TO LATER POSTS:
In the Meissner Nicolai context I don't think we are looking for conformal symmetry at the UV fixed point. I discussed that a bit in the other thread. Could be wrong, but I believe they are talking about a low energy flat space limit.

 

[Haelfix]

A UV fixed point of a field theory is conformal by definition. Different name for the same thing (alternatively, the beta function of the renormalization group is zero). There are several types of fixed points that are possible. In the case of the asymptotic safety proposal, the fixed point(s) in question are nongaussian. Asymptotic freedom is the case where the fixed point is gaussian (or trivial)

 

[atyy]

A UV fixed point of a field theory is conformal by definition. Different name for the same thing (alternatively, the beta function of the renormalization group is zero). There are several types of fixed points that are possible. In the case of the asymptotic safety proposal, the fixed point(s) in question are nongaussian. Asymptotic freedom is the case where the fixed point is gaussian (or trivial)

Thanks for clarifying! Is it also "conformal" in the sense of "conformal gravity"?

 

[atyy]

Nastase http://arxiv.org/abs/0712.0689
" There are two ways in which this can happen:
• β = 0 everywhere, which means a cancellation of Feynman diagrams that implies there are no infinities. OR
• a nontrivial interacting theory: the β function is nontrivial, but has a zero (fixed point) away from λ = 0, at which a nontrivial (nonperturbative) theory emerges: a conformal field theory. ........

Most theories that are quantum mechanically scale invariant (thus have β = 0), have a larger invariance, called conformal invariance."

Hamber http://arxiv.org/abs/0704.2895
"At the fixed point G = Gc the theory is scale invariant by definition. In statistical field theory language the fixed point corresponds to a phase transition, where the correlation length ξ = 1/m diverges and the theory becomes scale (conformally) invariant."

 

[atyy]

I wonder if the difference between Asymptotic Safety and conformal gravity or 't Hooft's proposal is that in the former gravity approaches the UV fixed point with increasing energy, while the latter postulates that gravity is at the fixed point. I guess like QCD is asymptotically free, not free.

 

[Finbar]

atyy,

My understanding is that at the UV fixed point Newtons constant will run as G= g/k^2. where g is the dimensionless Newtons constant for which $$\beta=0$$ at the fixed point and k is the energy scale such that k tending to infinity implies G tends too zero. This means that in a sense Newtons constant is free at the UV fixed point. This may well imply that whatever the "bare action" is that is being quantized is it will be conformal and there is no Einstein Hilbert term in it. But once it is quantized loop effects will induce an effective Einstein Hilbert term; hence gravity is emergent and conformal invariance is broken.

This is at least my take on how conformal gravity and asymptotically safe gravity may be two approaches to the same physics. AS really starts at the IR physics and uses the RG to push the theory to the UV; from the effective action to the bare action. Where as conformal gravity starts at the UV then quanitizes the theory hence moving from the UV to IR; from the bare action to the effective action.

The problem for the AS approach is the "re-construction problem" as Reuter calls it. Which is the problem that when you push the "effective average action" to infinity its not equal to the bare action i.e. one cannot see what microscopic degrees of freedom are being quantized.

this paper discusses the problem http://arxiv.org/abs/0905.4220