Monday 29 September 2008

Gia's Hairy Black Holes

Now that the hope for a quick LHC start-up has literally vaporized, I have six more months to play with particle theory without worrying about experimental constraints. This is a good moment to return to the workshop on black holes that is still trickling here at CERN. Last Friday, Gia Dvali was presenting his ideas concerning gravity theories with a large number of particle species. The subject is more than one year old and I already wrote about it in this blog. Gia is trying to derive general features of field theory coupled to gravity, without making specific assumptions about the underlying quantum gravity theory. To this end he produces gedanken black holes (at the LHC, or anywhere in the Universe) and employs unitarity plus general properties of semi-classical black holes to obtain some interesting conclusions.

In particular, Gia argued one year ago that in a theory with N species of particles there is a bound on the fundamental scale $M_*$ where the gravitational interactions become strong. Namely, the bound reads $M_* \leq M_P/\sqrt{N}$ where $M_P \sim 10^{19}$ GeV is the Planck scale as we know. This opens a possibility to solve the hierarchy problem by postulating $N = 10^{32}$ new particle species at TeV. One can immediately see the analogy to the ADD (as in Arkani-Hamed, Dimopoulos, Dvali) large extra dimensions. In ADD, the relation between the fundamental scale and the Planck scale is $M_P^2 = M_*^2 (M_* R)^n$, where n and R are the number and the radius of the extra dimensions. This relation is in fact equivalent to $M_* = M_P/\sqrt{N}$ because in ADD $(M_* R)^n$ is just the number of graviton KK modes below the cutoff of the theory. Gia argues that the ADD solution to the hierarchy problem is just one example in a larger class: gravity must become strong well below the Planck scale whenever there is a large number of particles species, regardless whether extra dimensions exist or not. The fact that in ADD the multitude of particles species are Kaluza-Klein modes of a higher dimensional graviton is just a red herring.

After the initial proposal Gia has posted several papers further developing this idea. On Friday Gia talked mostly about the consequences for black hole physics summarized in this paper. It turns out that micro black holes in theories with a large number of species have peculiar properties that make them quite distinct from ordinary black holes in Einsteinian gravity. First of all, small black holes with sizes of the order of $M_*^{-1}$ are hairy. This Freudian feature can be argued as follows. Consider a collision of a particle and an anti-particle of one species at center-of mass energies of order $M_*$. The production rate of micro black holes in that collision must also be of order $M_*$ because it is the only scale available. By unitarity, the decay into the same species must also proceed at the rate $M_*$. However, this cannot be true for the decay in the remaining N-1 species: the decay rate can be at most $\sim M_*/N$, while assuming a faster decay rate leads to a contradiction. For example, black hole exchange would lead to a too fast growth of scattering amplitudes that would be at odds with the assumption that the cut-off of the theory is at $M_*$. Thus, the micro black holes in a theory with N species are highly non-democratic, and they need to carry a memory of the process in which they were produced.

As black holes grow heavier and older they should start losing their hair. The scale where the Einsteinian behavior is recovered cannot however be smaller than $M_* N$. Thus, black holes in the mass range $M_P/\sqrt{N} < M_{BH} < M_P \sqrt{N}$ must be non-standard, hairy and undemocratic. The proper black hole behavior, which entails democratic decay to all available species via Hawking radiation, can be expected only for heavier black holes. Again, these properties can be readily understood in the specific example of ADD large extra dimensions as a consequence of the geometric structure of the extra dimensions (for example, the crossover scale to the Einsteinian behavior is related to the radius of the extra dimension). Gia's arguments just generalize it to any theory with a large number of particle species. It seems that some kind of "emergent geometry" and "localization" must be a feature of any consistent low scale quantum gravity theory.

Of course there is a lot of assumptions that enter in that game (no black hole remnants, for example), and it is not unthinkable that the true quantum gravity theory may violate some of these assumptions. Nevertheless, I find amusing that such simple hand-and-all-body-waving arguments lead to quite profound consequences.

More details in the paper.

Saturday 20 September 2008

AdS/CFT goes cold

Last week Dam Son gave two nice talks about phenomenological applications of AdS/CFT:
one about heavy ions, and the other about non-relativistic conformal field theories (CFTs). While the former application is widely discussed in pubs and blogs, the latter is a relatively new development. It seems that, after having entrenched in the heavy ion territory, particle theory has launched another offensive on the unsuspecting condensed matter folk. Not later than yesterday I saw two new papers on the subject posted on ArXiv.

AdS/CFT as we know it relates strongly coupled gauge theories to gravity theories in one more dimension. In the original tables received at Mount Sinai by Maldacena it speaks about highly symmetric and all-but-realistic theories: N = 4 super Yang-Mills on the gauge theory side and 10D type IIB supergravity in $AdS_5\times S_5$ background on the gravity side. Later, the correspondence was vulgarized to allow for phenomenological applications. In particular, some success was reported in postdicting meson spectra of low-energy QCD and explaining large viscosity of the quark-gluon plasma. Heavy ion collisions are total mess, however, and one would welcome an application in the field where the experimental conditions can be carefully tuned. Condensed matter physics enjoys that privilege and, moreover, laboratory systems near a critical point are often described by CFT. The point is that in most of the cases these are non-relativistic CFTs.

A commonly discussed example of a condensed matter system is the so-called fermions at unitarity (what's in the name?). This system can be experimentally realized as trapped cold atoms at the Feshbach resonance. Theoretically, it is described using a fermion field with the non-relativistic free lagrangian $\psi^\dagger \pa_t \psi - |\pa_x\psi|^2/2m$ and short range interactions provided by the four-fermion term $c_0 (\psi^\dagger \psi)^2$. The experimental conditions can be tuned such that $c_0$ is effectively infinite. In this limit the system has the same symmetry as the free theory and, in particular, it has scale invariance acting as $x \to \lambda x$, $t \to \lambda^2 x$. The full symmetry group includes also the non-relativistic Galilean transformations and special conformal transformations, and it is called the Schrodinger group (because it is the symmetry group of the Schrodinger equation). Most of the intuition from relativistic CFT (scaling dimensions, primary operators) carries over to the non-relativistic case.

The most important piece of evidence for the AdS/CFT correspondence is matching of the symmetries on both sides of the duality. For example, the relativistic conformal symmetry SO(2,4) of the SYM gauge theory in 4D is the same as the symmetry group of the AdS spacetime. In the case at hand we have a different symmetry group so we need a different geometric background on the gravity side. The Schrodinger group Sch(d) in d spatial dimensions can be embedded in the conformal group SO(d+2,2). For the interesting case d = 3 this shows that one should look for a deformation of the AdS background in six space-time dimensions, one more than in the relativistic case. In the paper from April this year, Dam Son identified the background with the desired symmetry properties. It goes like this
$ds^2 = \frac{-2 dx^+ dx^- + dx^i dx^i + dz^2}{z^2} - \frac{(dx^+)^2}{z^4}$.
The first term is the usual AdS metric, the last term is a deformation that reduces the symmetry down to the Schrodinger group Sch(d). The light-cone coordinate $x^-$ is compactified, and the quantized momentum along that coordinate is identified with the mass operator in the Schrodinger algebra.

So, the hypothesis is that fermions at unitarity have a dual description in terms of a gravity theory on that funny background. Many details of the correspondence are still unclear. One obstacle seems to be that fermions at unitarity do not have an expansion parameter analogous to the number of colors of relativistic gauge theories. A more precise formulation of the duality is clearly needed.

Friday 19 September 2008


Yesterday, CERN was buzzing with rumours that the first LHC collisions should take place during the week-end. This morning, however, there was a major quench in Sector 3-4. As you can see here, some magnets in the affected sector are now at almost 100K. LHC-progress addicts report that pretty scaring entries were appearing in the LHC logbook this morning (fire alarm, power failure, helium leaking into the tunnel), though all the record seems to be deleted now. Although there has been no official news so far, this problem appears to be serious (unlike all the problems reported by the media earlier this week) and may cause a lot of delay. It is not certain if operation will be resumed before the winter shutdown. So you can relax for the moment.

Update: there is a press release explaining what happened:
During commissioning (without beam) of the final LHC sector (sector 34) at high current for operation at 5 TeV, an incident occurred at mid-day on Friday 19 September resulting in a large helium leak into the tunnel. Preliminary investigations indicate that the most likely cause of the problem was a faulty electrical connection between two magnets which probably melted at high current leading to mechanical failure(...)
The crucial information is
(...)it is already clear that the sector will have to be warmed up for repairs to take place. This implies a minimum of two months down time for the LHC operation...
In fact, warming up and cooling of one sector usually takes 3 months, so there is little hope for a beam before the winter shutdown (end of November).

Update 2: :-(

Friday 12 September 2008

What will the LHC discover

The excitement generated by the LHC kick-off last week is still in the air. I'm beginning to realize that soon we will k.n.o.w. Which means that it's the last moment for gambling and wild guessing. Here are my expectations. The probabilities were computed using all currently available data and elaborated Bayesian statistics.

Higgs boson. Probability 80%
Peter Higgs' kid is ugly and problematic, however his big advantage is that he does his job right. Firstly, he knows how to break electroweak symmetry in such a way that the scattering amplitudes of W and Z bosons remain unitary at high energies. Secondly, if he is not much heavier than 100 GeV, he is consistent with stringent precision tests performed by LEP and Tevatron. No one else can achieve both without complicated gymnastics. That's why Higgs is the safest bet.

Non-SM Higgs boson. Probability 50%
The Standard Model uniquely predicts the couplings of the Higgs to all fermions and gauge bosons. From experience, these couplings are very sensitive to new physics in any form.That's why a precise measurement of the Higgs production cross section and all possible decay rates may be far more exciting than the discovery itself.

New Beyond SM Particles. Probability 50%
That's what particle physics is about, isn't it ;-) Almost any extension of the Standard Model that explains electroweak symmetry breaking predicts some particles in the TeV range. So it seems a good bet that we will see some of the junk. The question is if we will be able to make sense of the pattern that will reveal...

Strong Interactions. Probability 20%
Nature has repeated this scenario all over again: interactions between fundamental constituents become strong and new collective degrees of freedom emerge. Condensed matter physicists see it everyday in their laboratories. In particle physics, the theory of quarks and gluons knowns as QCD at low energies undergoes a transition to a confining phase where it is more adequately described by mesons and baryons. It is conceivable that some of the Standard Model particles also emerge in this manner from a TeV scale strongly interacting dynamics. The problem is that we should have already seen the hints of the composite structure in low-energy precision tests, flavor physics and so on, but we see none of that. The reason why the probability for this scenario remains relatively high is our shameful ignorance of strongly interacting dynamics -- we might have easily missed something.

Dark matter. Probability 5%
All hopes lie in numerology: a stable particle with a weak-scale mass and a typical weak annihilation cross-section of order 1 picobarn would have roughly the right thermal abundance to explain the observed dark matter abundance. If this is the right track, the LHC would grab the most important discovery in the history of collider physics. But we know dozens of other plausible scenarios where the dark matter particle is either too heavy or too weakly interacting to be discovered at the LHC.

Little Higgs and friends. Probability 1%
It is a plausible possibility that the Higgs boson is a pseudo-Goldstone boson whose mass is protected from radiative corrections by approximate global symmetries, a sort of mechanism we see at work in the pion sector of QCD. Proof-of-principle models have been constructed: Little Higgs and Gauge-Higgs unification scenarios. But they are all kind of elephants on elephants...

Supersymmetry. Probability 0.1%
Supersymmetry is just behind the corner. After the LHC she will just pick another corner to hide behind. Supersymmetry will of course be seen at the LHC, just like she was seen in all previous hadron colliders. But, once the data are well understood, she will take a leave and come back into hiding where she clearly feels more comfortable. Susy aficionados should not however be worried. The field will flourish as a new, vast and exciting parameter space above 3 TeV will open for exploration. The wealth of new experimental constraints from the LHC, satellite missions, and dark matter detection experiments will make the-allowed-parameter-space plots colorful and sexy.

Probability $e^{-S_{dragon}}$
This possibility was recently pointed out by Nima Arkani-Hamed. The laws of quantum mechanics allow anything to happen, albeit the probability may be exponentially suppressed for complicated (large entropy) objects. CERN officials maintain there is no imminent danger since the putative LHC dragons will be microscopic (small dragons have the smallest entropy, hence the largest probability to appear in particle collisions) and anyway they will quickly suffocate in the vacuum of the beam pipe. Some researchers, however, have expressed concerns that the dragons might survive, grow, burn ATLAS, kidnap ALICE and lock her in a tower. A more comprehensive study of the potential risks is underway.

Black Holes. Probability $0.1*e^{-S_{dragon}}$
Although microscopic black holes have smaller entropy than typical dragons, the advantage of the latter is that they are consistent with the established laws of physics, whereas TeV-scale black holes are not. There are many indirect arguments against TeV scale gravity, from precision tests, through flavor physics, to cosmology. Certainly, dragons are a bit safer bet.

Wednesday 10 September 2008

Day Zero Live

8.40. (Yawn). This is the day.
8.43. Yesterday was The End of the World Party downtown in Geneva. It was a quite success, though not as decadent as some might have hoped. On the picture, CERN theorists with WAGs.
8.46. It is certainly the beginning of the end of the world as we know it. Approximately in two years from now particle physics will be turned upside down. 99% of the currently fashionable particle physics models will go to trash. Maybe even 100% ?
8.50. The LHC is a black hole factory, and by exactly the same token it is also a time machine. From here one can peer into the future and read tomorrows newspaper. Here is a sample Thursday edition of an Italian newspaper (you may need to understand Italian and Italians to appreciate it):8.59 And here is the new logo of CERN:

9.05. The auditorium is 200% filled. The webcast does not seem to work. For the moment nothing's going on, just a scary movie on the big screen.
9.15. Lyn Evans explained the plan for the day. First, they are going to inject the beam at point 2 and dump it at point 3. Then they will remove the dumping block at point 3 and try to get to point 4. And so on, hopping octet by octet. When the tour is complete they will start circulating the beam.
9.25. They are injecting the beam and it reached point 3. Applause. People are still flowing toward the Auditorium. There are guards now at the entrance to turn back the crowd and avoid a stampede. Feels like Glastonbury 2000.
9.35. It is really amazing. 1000s of people are staring at the screen, after a few moment a dot appears in the middle and everybody's applauding. It must be the same feeling as watching a baseball game.
9.50. The beam is at point 5 now, and CMS may soon see some splashes. The control room looks like the NASA control room: topü figures staring with serious faces on blinking monitor screens, trying to make an impression everything's under control. Others obviously bored, since it's not allowed to play network games in the presence of TV cameras.
9.55. Meanwhile, the beam got to point 6. However it apparently needs some more manicure, pedicure and collimation before moving further along the ring. Good progress so far.
10.08. Point 7 reached. By the way, if you're having cold feet by now, this blog may provide reassurance.
10.12. Point 8, and then point 1. The circuit is almost complete. In a moment Atlas will see first events in their detector.
10.25. Last octet. Two dots on the screen, which means the beam has made a full clockwise circuit!!!
10.28. Well, well, it seems that the damn machine is working. That's quite unexpected.
10.40. Not much going on now. Music, champagne, interviews....If you are bored with this one, other live commentaries here, here and here.
11.01. In 1 hour or so they will try circulating the beam counterclockwise. Since parity is not conserved in the real world, things might be quite different in that case.
11.09. The picture of the first event in Atlas (thanks to Florian). No idea what's on it :-)
11.29 The tension has clearly dropped. For the last hours there's been only interviews (can't they think of other question than how do you feel?) and boring speeches. They should do something to pump it up. Like for example a mud fight between CMS and Atlas.
12.01. Lyn Evans and Robert Aymar are holding a triumphant press conference.
12.30. Yes! After the first beam we also got the first protester, who came all the way from Germany. He seems quite nice, and harmless, a bit confused too.
12.35. There's some problem with the cryogenic system of the magnets, so that the 2nd beam will be delayed.
13.55. Back after the lunch break. The magnets are cool again, the 2nd beam is being injected.
14.01. 2nd beam is at point 7, then point 6. OK, it's a bit less exciting than the first time...
14.15. Looks like they are having some problems with collimating the beam. They are stuck at point 6 until the beam gets smoothed out.
14.33. Operation resumed. They are at point 5 and passed the CMS detector. Everybody in the CMS control room felt a swoosh of wind.
15.02. Two spots on the screen! First full counterclockwise circuit. Applause, though shorter than for the first beam. It's always better to be the first than the second.
15.05. Robert Aymar said that it's working smooth as a roulette. I hope he didn't mean Russian roulette. Now they will try to get more than one circuit of the beam.
15.25. Basically, the plan for today has been accomplished. Today they will play a little bit more with the 2nd beam. The plan for the nearest feature: sustain the beam continuously, collide two beams at 450 GeV, accelarate the beam in the LHC ring.
16.35 Champagne in the control room. So there won't be more beam today ;-)
17.05. The first beam in the LHC: press release.
18.05. The webcast is now over. The end of the world live was a full success. Everything is going unexpectedly smoothly, so the first collisions may happen sooner than assumed. I'm going to sleep now, but the LHC is not: the work will continue tonight, and tomorrow is another working day (even though it's holiday in Geneva). What we were so excited about today, tomorrow will be just a boring routine. Good night and good luck.

Friday 5 September 2008

Final Countdown

So it's really kicking off...

I expect there will be party and celebration all over the world. Here in Geneva the locals are organizing The End of the World Party, Tuesday, September 9 in Lady Godiva, from 8pm untill the end. Surely, it's the end of the world as we know it...

Wednesday 3 September 2008

3D Games with Gravity

These days CERN is running a six-week long TH institute program on black holes. In the eve of the LHC, the subject receives a lot of attention in newspapers and on YouTube. Unfortunately, the Special Task Force Report proved that the LHC black holes are not capable of destroying the Earth, which deprives them of much of their charm. Nevertheless, black holes remain interesting because they are intimately related to many important questions in quantum mechanics, string theory, AdS/CFT and psychoanalysis.

The past week was dominated by "Big Issues", like the black hole information paradox. Big questions make me feel small, especially when no answers are provided. So instead, what I found most interesting was the talk of Wei Li about 3D gravity. That was hardly a big issue, but rather a cute piece of mathematical physics which relates here and there to black holes. The subject is currently going through a phase of accelerated expansion, even though it all happens in AdS.

3D gravity attracts some attention because it is simple enough to hope for an exact solution of the quantum theory, and at the same time it is complicated enough to maybe shed some light on 4D quantum gravity. At first sight, 3D is completely uninteresting. In D dimensions, a graviton has D(D-3)/2 degrees of freedom, which gives the usual 2 degrees of freedom in 4D, and zero degrees of freedom in 3D. However, it turns out that things are not that trivial. In the early nineties it was found that the Einstein gravity with a negative cosmological constant has black hole solutions -- the so-called BTZ black holes. Much like their their 4D cousins, 3D black holes possess everything a respectable black hole should possess: a horizon, Hawking temperature and entropy. This means that the quantum theory should contain microstates that make up the black hole and account for the entropy.

The common line of attack on 3D gravity goes via the dual conformal field theory (CFT). 3D gravity is a topological theory with its degrees of freedom living on the boundary of space-time. Long ago, Brown and Henneaux showed that the physical Hilbert space has an action of the Virasoro algebra corresponding to 2D CFT with the central charges $c_L = c_R = 3l/2G$ (G is the 3D Newton constant and 1/l parametrizes the cosmological constant, in case anybody is still reading). 2D CFTs have little mysteries, so identifying the dual CFT means solving the 3D quantum gravity. In particular, the microstates of the CFT explain the black hole entropy.

The quest for CFT is dangerous as one be eaten by the monster (group). To avoid Witten's fate, Wei Li and company took a different path. They studied the deformation of the 3D gravity called topologically massive gravity that, apart from the Einstein-Hilbert term and the cosmological constant, contains the Chern-Simons term $\sim \frac{1}{\mu} Tr (\Gamma d \Gamma + 2/3 \Gamma \Gamma \Gamma)$. Topologically massive gravity inherits all AdS and black hole solutions of Einstein gravity.

Wei Li and company argue that the theory is stable only for one special value of the parameter $\mu$. The Chern-Simons term modifies the central charges as $c_L = 3l/2G(1- 1/\mu l)$, $c_R = 3l/2G(1 + 1/\mu l)$. If $\mu l <> 1$ is also bad. The Chern-Simons term contains 3 derivatives term which changes the counting of degrees of freedom and, as the result, the theory contains a new degree of freedom -- a massive graviton. This excitation becomes a ghost (it has negative energy) for $\mu l > 1$.
Thus, the whole theory is sensible (at most) for $\mu l = 1$. This is a very special point since the dual CFT is chiral: $c_L = 0$, so that the CFT is holomorphic (contains only right-movers). Hence the name chiral gravity. So the conjecture is that the 3D topologically massive gravity is equivalent to 2D holomorphic CFT. It remains to be found which one.

Slides of all the institute talks are apparently beyond the horizon. Here you find the slides of the related talk by Andy Strominger at Strings'08.