There will be a school on quantum gravity this summer in Morelia, Mexico, from June 23rd to July the 3rd. Don Marolf, the chair of the event asked me to promote the event. The deadline for applications is January 31st (the end of this week).
There is also going to be a workshop on future directions in lattice gauge theory, this summer at CERN. This is of interest to me, but I don’t know if I will be able to make it or not.
Also, the deadline for the Aspen Center for Physics summer 2010 session is by the end of this week.
In the fall there will also be an interesting workshop on aspects of the AdS/CFT correspondence at the Galileo Galilei Institute for Theoretical Physics in Florence. Again, very interesting, but I don’t know if I will be able to make it.
Hi David,
Any chance you could blog about your new paper?
Thank you!
Hi Mark:
I plan to do so. Getting that paper out has been a preocupation of mine for the past few months.
How many people do they expect to attend, and is it possible to sit in if one is not a grad student or a post-doc?
HI Eugene:
I am not one of the organizers and don’t have access to this kind of information. Please contact the organizers directly.
Great! I look forward to it.
…hablando de Roma
“Quantum Gravity in the Southern Cone V”
http://www.fisica.unlp.edu.ar/strings/qgsc
Dear David, your paper is very interesting – a nice explicit, brute-force approach to similar issues.
But I actually don’t believe that the full N=4 SYM has such a slow/bad/non-convergent large-N behavior of the wave functionals etc. This must be a result of your truncations, for example the removal of fermions. Such a dependence on the calculational simplifications is always an issue with the numerical approaches etc.
Have you tried, for example, to replace 6 bosons by 22 bosons? That would describe the AdS theory with 22 real adjoint scalars which has a vanishing beta-function at one loop, much like N=4, but only at one loop. (Recall the -11/3 from the gauge field – and the CFT may also be interpreted as AdS5 x S21 of the bosonic string, with some grain of salt.)
I think that the convergence properties could be better.
However, you might also have to include the p-waves of some scalars, not just the s-wave (quantum mechanics), because otherwise the model only knows about a 0+1 dimensional theory, while only the 3+1 dimensional one has different properties.
Recall how carefully one must add various fermions etc. e.g. in Matrix theory in order to see the smooth emergent space at all. The zero-point energy of the harmonic oscillators is not canceled. In your non-convergent behavior, you may be just seeing unphysical things as mundane as uncanceled zero-point energies that are canceled in the full theory, etc.
Best wishes
Lubos
Hi Lubos:
We have tried varying the number of scalars and other things. Increasing the numbers of scalars tends to make matters worse. Mostly because one has to approximate a higher dimensional geometry with the same number of dots. I am really confused by the slow convergence of the results. In a sense, I don’t believe in my heart that it represents the true behavior, but the numbers have to be reported as they showed up and I couldn’t find an obvious problem with the data (you can complain that we didn’t do the best possible data analysis given the information, but this can only be judged a posteriori, whereas we had set a procedure a priori). Our lack of understanding of these issues has delayed this work and some other works in progress for quite a while.
I do believe many of the features that are found are artifacts of the truncations, but I don’t know which of them.
The main objective of the paper is to explore what does it mean to have emergent geometry, by brute force if necessary (it was necessary). Regarding divergences of moments of distributions, they show up in setups with non Gaussian behavior and obviously if you use those moments to define a measurement you get nonsense.
By the way, if anyone wants the code for generating distributions, they can have it. It is not user friendly however and some hacking might be required.
Dear David,
the things probably get worse with additional scalars because the “negative” contribution of the gauge field itself (besides fermion) – the signs proportional to those in the beta-function terms – are also omitted.
I don’t think it is any real discrepancy. Try to reverse-engineer what you did, with some more detail that becomes accessible from the opposite perspective. First, you didn’t approximate N=4 gauge theory.
It’s the pure bosonic theory – and you have omitted not only fermions but also the gauge field, kind of, right?
So take the (non-conformal) bosonic theory with 6 adjoint bosonic scalars only, and maybe in a wrong dimension. What is its AdS dual? What would you actually expect a similar analysis as yours to tell you about the geometry based on this AdS dual?
In my opinion, these duals are just mess. They’re not AdS because conformal symmetry is broken, beta function is nonzero. They don’t give you any sensible string backgrounds. For example, there’s no critical bosonic string theory in 10D. I think that to get AdS5 x S5, things really have to appreciate most of the details.
In other words, I think that there are many cancellations etc. that any inaccurate analysis can kill. Instead of Matrix theory, I should have mentioned BMN.
Take e.g. all the interactions between the BMN operators – how many kinds of cancellations and non-renormalization theorems you need to prove that some parasitic terms in the correlators – and even in the spectrum – cancel.
You can’t get these things for free, and you shouldn’t be surprised that you don’t get these things for free. This story has been with string theory since the 1980s. For example, N=1 SUGRA/super-Yang-Mills coupled system was certainly anomalous, producing lots of terms whose presence was almost guaranteed – and could have been even “proven” to be nonzero, killing virtually all hopes for a realistic chiral background based on string theory.
However, some extra terms from the Green-Schwarz mechanism were omitted. When added, cancellations were possible with a miracle – and indeed, the miracle was found to occur for the well-known gauge groups.
I feel that this fine-ness and “precise arrangement” of the theory is mostly ignored by the physics establishment again. Lessons of 1984 (not Orwell) are forgotten. It’s completely ignored by the alternative physics community. But even in the AdS/CFT, the atmosphere seems to be that “anything goes” once again. People don’t care whether they omit fermions or gauge fields, and think that everything will be unchanged, etc.
While gauge theory may have some universal features that don’t depend on these truncations, it has many more features that do depend on them, and I think that the bulk dual observables almost universally do depend on them.
Of course, the only way to find out what truncation causes what strange behavior is improve the accuracy of the analysis, so that the strange behaviors begin to disappear one by one.
Still, it’s true that many things had cancelled from the scratch. In Matrix theory, Tom Banks and others would propose that the scattering amplitudes as a function of “N” would have a strange behavior, and one would actually need N-dependent subtractions (“counterterms”) to define the large N limit. I have always disagreed, being convinced that BFSS was physical light-cone gauge even at finite N (which Lenny finally published in “his” article, too).
But it’s fair to say that all these things could only work at finite N because of SUSY cancellations. I wouldn’t expect anything on the strongly coupled dual side to be manifestly working at finite N when you completely break SUSY. The only “moral” toy model where the geometry could work fine is a non-supersymmetric model of the duality, in d=2 gravity and “old matrix models”, but over there, it does work, right?
Best wishes
LM
Hi Lubos:
Thank you for your reminders of the issues that one has to deal with. In our case fermion and boson cancellations were taken into account to get to the commuting matrix model a long time ago, this included the vector particles. This is captured by not having zero point energies of the off-diagonal bosons (they have been cancelled with other modes). This does not mean that a full calculation has actually shown that all of this stuff cancels in the measure terms, this is just some approximation to take into account cancellations, because all these degrees of freedom are technically very heavy and the masses of bosons and fermions are essentially degenerate. The zero mode of gauge transformations is special, and that determines the volume of the gauge orbit of the commuting configurations. This does not cancel: there are no zero modes for fermions on the sphere. The end model is not even the commutator squared potential, but much less.
The question I was asking with the student I was working with was not whether this is an accurate model of N=4 SYM. Instead, even though it is a huge simplification with a lot of stuff thrown away, it is a model that still exhibits emergent geometry behavior that is related in some way to the full emergent geometry of N=4 SYM.
The question we were trying to determine is how do we measure a metric distance property in such a model, with everything fluctuating, and how large does N have to be before results start looking nice.
We were not trying to be fancy. Quite the contrary. If I actually knew how to solve the full strong coupling SYM theory and how to derive the ten dimensional geometry I would have done so
Sadly, even though that is what I want, I don’t know how to do it yet 