Reuter takes hit, Hamber says Lambda can't run

marcus

Yes. Look on page 30 where they devote a paragraph to critiquing Reuter AS. Leading up to page 30 they cite Reuter and Litim papers: references [25], [26], [27]. They describe salient features of the approach. Then on page 30 they say there are two problems with it. But they actually give three problems. The second problem is that (according to them) it is inconsistent with general covariance, for the reason discussed in this thread.

Haelfix

One has to be a little bit careful here. The definitions of lambda(k) and G(k) in general differ substantially between the classical theory, the usual quantum gravity procedure utilized by eg , 'T Hooft, Donaghue and Hamber, the functional renormalization group approach utilized by Reuter and older asymptotic safety proposals and methods from the 90s.

In general, these terms are regularization and renormalization scheme dependant, even before truncation approximations are utilized.

This of course makes perfect sense, b/c G is dimensionful, so people organize the energy expansion in such a way as to find some (any) dimensionless coupling to expand about. This of course requires G and two powers of mass, so something like G(k^2). So it is something like G (cutoff)^2 that could *potentially* run, never the actual bare Newton's constant. Of course the details will differ up to field redefinitions.

Now, the actual running and renormalization of these quantities is very subtle business, and different authors organize the problem in mathematically different ways. Which leads to a problem with making a naive comparison between quantities that are no longer trivially related.

Also there have always been technical issues with the functional renormalization group approach (incompatibility between the IR and UV cutoffs, the violence of the truncation to the divergence structure of the theory, how terms are absorbed into the definition of the running coupling constant etc etc). Anyway all of this is far from settled. So there is not necessarily a disagreement (although Hamber does think that there is) in principle, but it does require more careful work.

Anyway, these are all technical problems, perhaps in principle fixable. There are much more serious physical problems with the theory. Namely the fact that conformal field theories dof and entropy counting scales as the volume, and not as the area (as you would expect a general theory of quantum gravity in the deep UV to behave as). This violent clash with Black hole thermodynamics is not fixable and is a prediction of the theory (one that seems violently at odds with how we understand black hole physics). Likewise, locality is always manifest in AS and not broken. This is also at odds with the blackhole information loss

atyy

Is the Hamber/Reuter difference something like a renormalization scheme dependence (ignoring the truncation issue)?

Edit: Yes, it seems from Haelfix's post just above this.

I remember seeing another interesting paper about renormalization scheme dependence in quantum gravity recently http://arxiv.org/abs/1211.1729

marcus

Let me see if I can spell it out. Hamber specifically targets Reuter AS and refers to several representative Reuter papers. Let's study what he actually says. That should answer your question in the least vague least interpretational way.
Here is the relevant paragraph.
==quote Hamber Toriumi p. 30==
...A nontrivial fixed point in both couplings (G∗,λ∗) is then found in four dimensions, generally with complex relevant eigenvalues ν−1, with some dependence on the gauge parameters [26].
There seem to be two problems with the above approach (apart from the reliability and convergence of the truncation procedure, which is an entirely separate issue). The first problem is an explicit violation of the scaling properties of the gravitational functional integral, see Eqs. (6),(7) and (8) in the continuum, and of the corresponding result in the lattice theory of gravity, Eq. (53). As a result of this conflict, it seems now possible to find spurious gauge-dependent separate renormalization group trajectories for G(k) and λ(k), in disagreement with the arguments presented previously in this paper, including the explicit gauge-independence of the perturbative result of Eq. (36). In light of these issues, it would seem that the RG trajectory for the dimensionless combination G(k)λ(k) should be regarded as more trustworthy. The second problem is that the running of λ(k) claimed in this approach seems accidental, presumably due to the diffeomorphism violating cutoff, which allows such a running in spite of the fact that, as we have shown, the latter is inconsistent with general covariance. One additional and somewhat unrelated problem is the fact that the above method, at least in its present implementation, is essentially perturbative and still relies on the weak field expansion. It is therefore unclear how such a method could possibly give rise to an explicit nonperturbative correlation length ξ [see Eq. (40)], which after all is non-analytic in G.
==endquote==

atyy

Honestly, seems like no big deal. Hasn't Hamber's AS has differed from Reuter AS for many years? I believe the lambda issue is already mentioned in passing in the old Hamber papers.

Eg. in the new paper "The same is found to be true in the lattice formulation of gravity, where again the bare cosmological can be scaled out, and thus set equal to one in units of the ultraviolet cutoff without any loss of generality. One concludes therefore that a running of lambda is meaningless in either formulation." http://arxiv.org/abs/1301.6259 p2

In the old paper "by a suitable rescaling of the metric, or the edge lengths in the discrete case, one can set the cosmological constant to unity in units of the cutoff. The remaining coupling G should then be viewed more appropriately as the gravitational constant in units of the cosmological constant λ." http://arxiv.org/abs/0901.0964 p55

marcus

That's your interpretation based on your sense of proportion. For you Hamber's persistence makes his objection less significant. For me, more.

It looks to me as if he has raised the ante by devoting a paper to proving that having the two couplings run separately is inconsistent with general covariance. He apparently is convinced that it is the dimensionless product λG that should do the running, if anything does.

If you like, call that "G in units of one over λ". One over λ is an area, and if you set c and hbar equal to one then G is naturally an area quantity---so can be expressed in terms of 1/λ. You quoted Hamber saying something to that effect.

Anyway you may be paying too much attention to the "politics" of who is pro-this and con-that. I've long been a fan of Shaposhnikov, and minimalist approaches, and of AsymSafe QG particularly as presented by Percacci, and occasionally by Saueressig, and Reuter. I've never been an enthusiast for Hamber's work. But I think Hamber may have proved something and I have to take the possibility seriously.

It may turn out to be a false alarm and be dismissed. But if not, if it is confirmed, then I expect some kind of tectonic shift in AS---maybe a move in the direction Finbar suggested:
AS with Unimodular rather than standard AS---viz the paper by Astrid Eichhorn. And I would also expect (if this critique of standard AS is upheld) for Shaposhnikov to modify what he says and take a somewhat different tack.

So at this point I won't dismiss the paper as you do, and say it is "no big deal"
I'll probably wait and see a little on this one.

atyy

I don't think it will move it towards unimodular AS, since Hamber has been saying this a long time. I have felt the same respect for Hamber as for Percacci, Reuter, Litim etc.

Anyway, maybe it'd for me be better to say no new deal, rather than no big deal.

What's unclear to me is whether Hamber's method gets any closer to showing AS than eg. Percacci. It seems to me all the AS papers have problems, OTOH there are also no non-handwavy arguments against AS.

John86

Will this in one way or another mean that the AS framework will be les minimalist

atyy

I don't think so. Hamber is a proponent of AS. He's been having a non-running "cosmological constant" since at least 2007. http://arxiv.org/abs/0704.2895 "The remaining coupling G should then be viewed more appropriately as the gravitational constant in units of the cosmological constant λ". In that paper he also discusses the "non-trivial fixed point" that is characeristic of the simplest versions of AS.

I think the question of minimal or non-minimal within AS has to be about the matter content. It's not clear whether any version of AS exists at all, or whether there are many versions of AS each with different matter. The Shaposhnikov and Wetterich proposal assumes AS and is minimalist in matter content - one could discuss whether Hamber's conclusions affect that proposal. I think one should be careful in comparing Hamber's scheme and Shaposhnikov's, and whether the operational definitions of the various quantities having the same name are also the same. I believe this is what Haelfix's post #19 is also saying.

Eg. Shaposhinkov and Wetterich's footnote 1 says "We would like to stress that the definition of the running couplings here is based on the gauge-invariant high energy physical scattering amplitudes [1], rather than on the minimal subtraction (MS) scheme of the dimensional regularization. In the MS scheme perturbative Einstein gravity does not contribute to the β functions of the Standard Model couplings [13]" Ref [13] is http://arxiv.org/abs/0710.1002 .

In another but similar context, http://arxiv.org/abs/1209.3511 says "Despite having a pre-history[32], recent activity stems from the work of Robinson and Wilczek[33], who suggested that the beta function of a gauge theory could have the form .... While this correction is tiny for most energies, the negative sign suggests that all couplings could be asymptotically free if naively extrapolated past the Planck scale. Subsequent work by several authors, all using dimensional regularization, found that the gravitational correction to the running coupling vanishes[34]. Further work, including some of the same authors, using variations of cutoff (Λ) regularization then found that it does run[35], .... Papers trying to clarify this muddle include[36, 37, 38, 39]. My treatment here most naturally follows the ones of my collaborators and myself[36, 37]"

http://arxiv.org/abs/1111.2875 and http://arxiv.org/abs/1209.3511 are probably the most problematic for AS, since it seems to contradict all versions of AS, even Hamber's. However, the authors stop short of this conclusion, and says it deserves further study. I believe Anber and Donoghue do not rule out AS, but show that its ability to predict will be very restricted unless the exact matter content is known. The problem with AS being non-predictive without knowing matter is established and discussed by Percacci.

In http://arxiv.org/abs/0910.5390 Gurain and Percacci discuss renormalization scheme dependence.

In http://arxiv.org/abs/0910.5167 Percacci says "Of course I am not claiming here that equations (64) are to be taken literally as the correct predictions: there is too much that we are neglecting in the calculations. However it seems possible that with more effort the asymptotic safety program will eventually produce realistic predictions."

I think Anber and Donoghue suggest the problem may be much worse than Percacci had hoped.