A workshop in Paris/Saclay is taking place this week entitled Wonders of Gauge Theory and Supergravity and the talks are now online. They show that some exciting new things have been happening in the study of gauge theory and supergravity amplitudes, and I’ll make the prediction that this field will attract a huge amount of attention in the coming years (at least until the LHC experiments announce results incompatible with the Standard Model…).

Perhaps the most remarkable part of this whole story is the mounting evidence that N=8 supergravity amplitudes are finite in perturbation theory. Remember the standard story about how quantum theory and general relativity are incompatible that has dominated discussion of fundamental physics for years now? Well, it turns out that this quite possibly is just simply wrong. See Zvi Bern’s talk on UV properties of N=8 supergravity at 3 loops and beyond for the latest about this. Bern shows that divergences everyone had been expecting to occur at 3 loops aren’t there, and gives evidence that they might also be absent at higher loops. He even sees this as a phenomenon not special to N=8 supergravity, but also occurring in theories with less supersymmetry, e.g. the N=5 and N=6 theories. Among the other talks, Nima Arkani-Hamed’s is also about this, advertising the idea that N=8 supergravity is the Simplest QFT.

Much of this story is about the N=4 SYM amplitudes and new insights into them and their relations to supergravity amplitudes, with some of this research growing out of and motivated by the AdS/CFT conjecture of the existence of a string dual to N=4 SYM. Quite a few of the talks are interesting and worth trying to follow, with a much higher proportion of new ideas than is usual at particle theory workshops in recent years.

To go out on a limb and make an absurdly bold guess about where this is all going, I’ll predict that sooner or later some variant (“twisted”?) version of N=8 supergravity will be found, which will provide a finite theory of quantum gravity, unified together with the standard model gauge theory. Stephen Hawking’s 1980 inaugural lecture will be seen to be not so far off the truth. The problems with trying to fit the standard model into N=8 supergravity are well known, and in any case conventional supersymmetric extensions of the standard model have not been very successful (and I’m guessing that the LHC will kill them off for good). So, some so-far-unknown variant will be needed. String theory will turn out to play a useful role in providing a dual picture of the theory, useful at strong coupling, but for most of what we still don’t understand about the SM, it is getting the weak coupling story right that matters, and for this quantum fields are the right objects. The dominance of the subject for more than 20 years by complicated and unsuccessful schemes to somehow extract the SM out of the extra 6 or 7 dimensions of critical string/M-theory will come to be seen as a hard-to-understand embarassment, and the multiverse will revert to the philosophers.

Many of the titles of the talks at Strings 2008 have recently been announced. The plenary talks will include several talks mostly not about string theory, including 3 about the LHC and one by Lance Dixon on the amplitudes story. It seems that the string theory anthropic landscape is a topic the conference organizers don’t want anything to do with, since the only person from the Stanford contingent speaking will be Kallosh on prospects for getting something observable out of string cosmology models of inflation. As for what is popular, it clearly helps a lot to be from one of my alma maters, with Princeton (7 speakers), and Harvard (3 speakers) the best-represented institutions.

**Update**: For an extensive rant about this, see here.

**Update:** Last week was Paris, this week it’s Zurich. Amplitudes are all the rage this summer.

“The “10^60″ number one sees refers to SSYM, where supersymmetry breaking will introduce a CC of the wrong scale. I think supersymmetry breaking is already a deadly problem for conventional SSYM models, this is just one more reason not to believe them.”

Of course you are ignoring supergravity theories where the cc can easily be fine-tuned, or in the case of no-scale supergravity, the vacuum energy automatically vanishes at tree-level.

Peter, regarding your reply:

“You really need some way of putting QFT together with GR to make the question of calculating the CC a well-posed one.”

I’d like to suggest that this is precisely the source of misunderstanding defining the CC problem. Vacuum in GR is an idealized cosmic state devoid of matter and energy. On the contrary, QFT vacuum is a quantum state embodying the contribution of all zero-point fluctuations. There is no compelling argument for relating the two concepts in a meaningful way.

Best regards,

Observer

Eric,

It’s rather well-known that the CC problem is not that it can’t be fine-tuned, but that it has to be.

Peter,

All that means is that the theory we are using is an effective theory. It’s really no different than having to fine-tune the masses of quarks and leptons in the Standard Model.

Peter:

It seems like that the CC problem is to be treated as just a renormaliztion issue as is the mass and charge of the bare electron in QED. Correct? But the bigger question is: Is QFT a fundementally correct approach if a basic calculation is so wrong? If QFT is deemed to be fundemental correct what mechanism(s) would potentially have to be included in some extention of the SM to avoid this problem (fine tuning)?

p falor,

All I’m doing is repeating myself at this point, but again:

1. The “CC problem” is ill-posed unless you have a viable unified theory. We don’t.

2. Naive expectations about what the scale of the CC would be in various possible unified theories lead to a completely wrong scale.

Personally, I don’t think one can conclude anything very interesting from 1. and 2.

There is a new interesting paper from Arkani-Hamed, and collaborators, “What is the Simplest Quantum Field Theory”, http://arxiv.org/PS_cache/arxiv/pdf/0808/0808.1446v1.pdf. It has interesting claims :

“Both tree and 1-loop amplitudes for maximally supersymmetric theories can be completely determined by their leading singularities, it is natural to conjecture that this property holds to all orders of perturbation theor. This is the nicest analytic structure amplitudes could possibly have, and if true, would directly imply the perturbative finiteness of N = 8 SUGRA. All these remarkable properties of scattering amplitudes call for an explanation in terms of a “weak-weak” dual formulation of QFT, a holographic dual of flat space.