## Wednesday, August 20, 2014 ... //

Natalie Wolchover wrote a good article for the Simons Foundation,

At Multiverse Impasse, a New Theory of Scale
about Agravity, a provoking paper by Alberto Salvio and Alessandro Strumia. Incidentally, has anyone noticed that Strumia is Joe Polchinski's twin brother? The similarity goes beyond the favorite color of the shirt and pants.

At any rate, the system of ideas known as "naturalness" seems to marginally conflict with the experiments and things may be getting worse. Roughly speaking, naturalness wants dimensionful parameters (masses) to be comparable unless there is an increased symmetry when they're not comparable. But the Higgs boson is clearly much lighter than the Planck scale and in 2015, the LHC may show (but doesn't have to show!) that there are no light superpartners that help to make the lightness natural.

The "agravity" approach, if true, eliminates these naturalness problems because according to its scheme of things, there is no fundamental scale in Nature. One tries to get all the terms in the Lagrangian with some dimensionful couplings from terms that have no dimensionful couplings. "Agravity" is a different solution to these problems than both "naturalness" and "multiverse" – a third way, if you wish.

Similar things have been tried before, e.g. by William Bardeen in 1995, but Strumia et al. are the first ones who are trying to add gravity. The claim is that one may get the Einstein-Hilbert action by a dynamical process in a theory whose terms only include four-derivative terms such as $$R^2$$.

Aside from a novel solution of the problems with the hierarchies, it is claimed that the scenario may predict inflation with the spectral index and the tensor-to-scalar ratio immensely compatible with the BICEP2 results.

The main obvious problem are the ghosts. The terms like $$R^2$$ may be rewritten as propagating degrees of freedom whose squared normal (sign of the kinetic term) are indefinite – some of them lead to proper positive probabilities while others produce pathological negative probabilities.

I remember a 2001 Santa Barbara talk by Stephen Hawking about "how he befriended ghosts", with some pretty amusing multimedia involving ghosts hugging his wheelchair, so you should be sure that Strumia et al. aren't the first folks who want to befriend ghosts.

At this moment, ghosts look like a lethal flaw. But I can imagine that by some clever technical or conceptual tricks, this flaw could perhaps be cured. The physical probabilities could become positive if one chose some better degrees of freedom, or there could be a new argument why these negative probabilities are ultimately harmless for some reason I can't quite imagine at this moment.

However, my concerns about the theory go beyond the problem with the ghosts. I do think that the Planck scale has been made extremely important by the modern "holographic" research of quantum gravity. The Planck area defines the minimum area where nontrivial information may be squeezed. It seems to be the scale that determines the nonlocalities and breakdown of the normal geometric concepts. The Planck scale is the minimum distance where a dynamical, gravitating space may start to emerge.

So if someone envisions some smooth ordinary spacetime at ultratiny, sub-Planckian distances, he is facing exactly the same difficulties – I would say that many of them are lethal ones – as the difficulties mentioned in the context of Weinberg's asymptotic safety which also envisions a scale-invariant theory underlying gravity at ultrashort distances.

There could be some amazing advance that cures these serious diseases but such a cure remains a wishful thinking at this point. We shouldn't pretend that the diseases have already been cured – even though you may use this proposition as a "working hypothesis" and a "big motivator" whenever you try to do some research related to agravity. That's why I find the existing proposals of scale-invariant underpinnings of quantum gravity, including the agravity meme, to be very unlikely. Hierarchy-like problems including the cosmological constant problem may look rather serious but they're still less serious than predicting negative probabilities of physical processes.

#### snail feedback (27) :

How is that different from conformal Gravity?

A good question, Giotis. ;-)

I just hunched that as the HEP sector of the knowledge-accumulating process of Science paints itself into a corner many of its participants will become desperate and come up with all sorts of 'radically different rationals' to brake free from the the constraints imposed by the strength of string/M theory.

Can we obtain this mechanism in string theory? That would certainly take care of the ghosts and make the idea more viable and compelling in the grander scheme of things. Conversely, it would be a coffin nail if that's not possible.

Never say never, but I would surely say that this is utterly incompatible with string theory. In perturbative string theory, one really can't avoid the string scale "alpha prime" encoded in the string tension, either.

One could discuss various "alpha prime equals zero or infinity" limits of string theory. But they either produce just the low-energy effective theories beneath the string scale, or theories with an exponential tower of massless states etc.

I also think that string theory avoids ghosts not only in the final product but at every intermediate step. In the light-cone-gauge, it can be formulated so that ghosts are never a part of the spectrum. That's why I can't imagine how this whole paradigm that at least "somewhat" allows ghosts could be compatible with anything I have associated with string theory. I am using these careful or vague comments because we don't have the most general and universal definition of string theory we would like to have so the claims can't be rigorous theorems but at least the spirits seem to be completely incompatible.

It is different that conformal gravity because they detune the combination of R^2 and R_{\mu\nu}^2that would make the action conformal. In fact, I believe they have only scale invariance.

Awkwardly, they had in version 1 a reference to B. Mussolini, the Italian dictator. Thank god, it is no longer there in version 2.

LOL, on page 23 of

http://arxiv.org/pdf/1403.4226v1.pdf

right before "shut up and compute" by Feynman. Are they fans of duce? ;-)

Is the situation with the ghosts analogous to the one in string theory before it was realized it works in 26 dimensions?

No, 26D bosonic string theory contains no ghosts. You must have confused them with tachyons.

Ghosts have the wrong sign of the kinetic term partial_mu PHI partial^mu PHI. Tachyons only have the wrong sign of the potential/mass term PHI^2 / 2.

I don't think they are fun of Mussolini. I believe that they just wanted to be provocative and attract curious readers.

A better translation of 'me ne frego' is 'I don't care' or perhaps 'I don't give a damn'

The quote linked to a satire where fascists conquered Mars solving the issue of the lack of air by beliving in the Mussolini slogan. It is a 2 layer joke

I was thinking more in terms of how it was considered possibly inconsistent and how that was eventually resolved; not specifically about ghosts or tachyons

Right, outside D=26, string theory had ghosts. But there was a potential for these things to decouple - become unphysical - and indeed, they do disappear in D=26.

However, the ghosts from the R^2 action don't seem to have the potential to disappear. They're as robustly present as the positive-norm states. 50:50

Ok, that answers the question I had in mind but apparently couldn't formulate well enough initially :) Thanks!

Hi Lubos: A question for my understanding- Does the conformal gravity theory also have the ghost problem? What about conformal field theory in general?

Yes, conformal gravity has ghosts by default. Look e.g. how Maldacena would fight them:

http://arxiv.org/pdf/1105.5632.pdf

No, (physical) conformal field theory doesn't have ghosts; they're (CFTs are) as physical theories as you may get in AdS/CFT or string theory. Conformal gravity is *not* a special case of a conformal field theory. A quantum theory of gravity isn't really a quantum field theory (in the same spacetime), so the inclusion you suggested is wrong even without the word "conformal".

Thanks Lubos.

Hello. Do you believe in Bardeen's argument that classical scale invariance solves the hierarchy problem? That argument is a motivation for agravity.

I though the minimal length/time of the Planck scale was defined by light(C) so that in order to have something smaller in terms of time or length you need to break the barrier of light(so lengths and times smaller than the planck length make no sense/are not detectable) How do they get around this? Throw out this whole conceptual scheme?

Great question. I didn't want to be too negative but my answer is Not really.

The beef of the hierarchy problem really arises from the quantum fluctuations so a property of a theory before its quantum corrections are taken into account doesn't seem to affect the behavior of quantum corrections and those matter for the origin of the hierarchies.

Moreover, the hierarchy problem really means that one has to fine-tune the parameters at the high energy scale. At that scale, e.g. Planck scale, as well as at any scale where something happens, the scale invariance is violated maximally - like QCD scale invariance at the QCD scale. When the scale invariance is such a bad approximation, so is the classical description.

At the end, I have some doubts whether it makes a deeper sense to distinguish explicit and "spontaneous" violation of scale invariance, anyway.

A very interesting paper, indeed. There is another recent paper by Hagen Kleinert that points in the same direction. He starts out with conformal gravity and gets Einstein gravity through "fluctuations" à la Coleman-Weinberg:
Conformal Gravity with Fluctuation-Induced Einstein Behavior at Long Distances.
He argues that one can shift the ghosts to high enough energies such that they don't matter in the same vein as the Landau pole.
The author makes an interesting claim at the end:
"The spontaneous generation of an Einstein action pro-
posed in this letter seems to be a much more satisfactory
way towards a physically acceptable quantum gravity."
Any opinions ?

Is negative probabilities different from mathematical inconsistency?

Can't the plank scale appear from no scale by something like dimensional transmutation? Another question off the topic: dimensional transmutation appear always at a lower energy scale. Can the opposite happen? I mean you start of a theory which has no scale at low energy but it gets a scale through dimensional transmutation at higher energy?

No.
"Negative energies and probabilities should not be considered as nonsense. They are well-defined concepts mathematically, like a negative of money." (Paul Dirac)
http://en.wikipedia.org/wiki/Negative_probability