## Thursday, November 04, 2010 ... /////

### Does quantum gravity make QED asymptotically free?

Nature is clearly not an expert journal for high-energy physics or a source of the most important articles. We've seen another piece of evidence for this fact yesterday. You may have read some hype about a paper freshly published in Nature:

Gravity shows its helpful side (Nature, review)

Toms, D. J. Nature 468, 56-59 (2010) (the technical article, link goes to the preprint on the arXiv)

Quantum gravity corrects QED (Physics World)
The last article even claims that the citations of this article are going to go into the stratosphere. Wow. Not bad. ;-)

Needless to say, while the paper is probably just an OK piece of work that could be used as the official solution to a homework in a quantum field theory course, this ambitious statement is preposterous and the preprint is going to be a low-citation preprint. I am more than eager to make a bet that it will be below 100 cits in one year.

What is the paper all about? The author has calculated a one-loop diagram correcting the fine-structure constant that includes some gravity propagators. This has been done (or tried) before, with some persistent confusion about the gauge symmetries and gauge independence, and Toms has arguably fixed it.

The previous papers that remained somewhat ambiguous about the gauge symmetries included Daum, Harst, Reuter from May 2010 which is just receiving its first citation today from Toms' work which seems to be just a relatively minor followup.

To make the story short, it's being shown that the beta-function for the electric charge has an extra term, so that it is
beta(E,e) = e3 / 12 pi2 -
- kappa2e / 32 pi2 (E2+3 Lambda/2)
I have deliberately copied equation (24) from Toms' paper, including the ludicrously sloppy negligence of the other terms in the beta-function. The formula above contains a usual 1-loop term from QED and another, negative term on the second line. The negative term goes like the squared energy in the units of Planck energy. Note that "kappa" is something like "1/E_{Planck}".

When does the beta-function become negative? Well, clearly, the second term has to be nominally larger than the first one, so the energy in the Planck unit must exceed "e^2" or the fine-structure constant. Because the fine-structure constant is near something like "1/25" at Planckian energies, the energy at which the negative term could prevail is something like "1/5" of the Planck scale.

But long before you get to these huge energies, you encounter all the other particle physics, including other charged fermions, the electroweak unification (at very low energies) and everything it brings, perhaps SUSY, GUT, and perhaps others. Even if you imagined that electromagnetism and gravity were everything that existed, the formula above still neglects all the two-loop and multi-loop QED corrections (which are still larger than the gravity term) and the negative term would be useless for making QED asymptotically free because it only comes from gravity which starts to produce its own divergences - worse than the Landau pole-like problems of QED because the gravitational divergences hurt even perturbatively - near the Planck scale where we really stand.

Moreover, in the real world, the Landau pole of the gauge theories (QED) would only appear at vastly trans-Planckian energies where the one-loop approximation would be surely wrong, anyway.

So the proposition that gravity can make QED more consistent is just an artifact of one term in some equations that is ludicrously taken out of the context and at least morally speaking, it is just totally wrong. Toms also says that with extra dimensions, the new term could be measurable by the LHC. Well, yes, the running would be measurable if the higher-dimensional Planck scale were much closer. But if it were the case, we could also observe many other, more spectacular effects of quantum gravity (and extra dimensions).

Also, he links the preprint to the weak gravity conjecture by Nima Arkani-Hamed, Cumrun Vafa, Alberto Nicolis, and your humble correspondent. He thinks that there is an "intriguing connection". However, the connection may imply something else than he wants for his paper to be important - and he seems aware of it.

The weak gravity conjecture says that gravity is the weakest force. In this context, it is almost exactly equivalent to saying that the new, negative term proportional to Newton's constant has to be nominally smaller than the first, positive term whenever we're below the mass scales given by new particles' masses (if we're above, we would have to include new terms in the beta-function). So the weak gravity conjecture actually and exactly implies that the term studied by the Toms paper is not important. ;-) Sorry for that.

Nature and unfortunately also Physics World show how easily science slips off the track and how not-the-most-appropriate papers may be overhyped if the selection process is not under good control. If the gauge issues are dealt with correctly, which I haven't checked, it's a good paper but it's ludicrous to suggest that it is an exceptional paper.

It kind of reminds me of the coefficient of the greenhouse effect. Some severely limited people are told that the influence of CO2 on temperature is nonzero - well, the influence of anything on almost anything else is nonzero - and by forgetting the rest of the science, they conclude that the greenhouse effect is important even in politics.

Cherry-picking and overhyping of convenient terms in equations is important for pseudoscientific propaganda.

Hat tip: Tom Weidig