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...

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.

Hot Photos of PAMELA

There's been some buzzing earlier this month about the new results from the satellite experiment PAMELA who measures the cosmic flux of anti-particles. Nature had a news story which said that positrons in the 10-60 GeV range show a large excess over the background. If the background is correctly estimated (rather unheard of in astrophysics), this could be an indirect sign of dark matter annihilation in our galaxy. The results from PAMELA were flashed during ICHEP and other conferences. However, due to the fact that the collaboration is publishing in Nature, there’s an embargo on releasing the plots in advance of publication. Congratulations to the Nature team for the idea, though they should acknowledge the Chinese government for the inspiration.

Fortunately, everyone can now find out what PAMELA's results are thanks to the authors of this paper. A footnote explain that

the data points shown in our figure have been graphically extracted from a photo of a slide shown by M. Boezio at the IDM08 conference, Stochkolm, 20/08/2008

Clearly, this adds some James Bond flavor to astroparticle research. Here are the pictures in all their beauty:
Thanks to Bob for the news.

Update: The story unfolds. Yesterday PAMELA's talk at CERN was "postponed due to Nature embargo". In retaliation, the latest volume of Nature laid out in the TH common room has been stained with coffee. Read also here and here.

String 2008 Summary

My winners in the most prestigious categories.

• Best Talk: Fernando Alday on Scattering Amplitudes via AdS/CFT . The word of the Lord, though always faithful, may be vague and subject to interpretation. Fortunately, PR stuff like annunciations and revelations is sometimes handed over to His seraphims who are able to beautifully explain a difficult technical subject. Plus a lilting Argentinian accent as a bonus in the live version.
• Worst Talk: Renata Kallosh on String Theory and Cosmology. A speaker with little to say and little communication skills is a common sight. Changing to an orthogonal subject in the middle of the talk added a new quality and has won her this competition.
• Best Review Talk: Lance Dixon on Structure of Amplitudes in Gauge Theory and Gravity, described here at more length.
• Best Mobile Ringtone: Andy Strominger with the Pink Panther theme.
• Best Performance: Shiraz Minwalla. To communicate his message, he uses four octaves and massive body language techniques. Some of the figures might have earned him a medal in the Beijing gymnastics competition. If you're not on the floor you may notice that the scientific part is very good too.
• Toughest Computation: Romek Janik, with the anomalous dimension of the Konishi operator tr$\Phi_i^2$ at 4 loops on the gravity side of AdS/CFT. All he got for his effort who a scolding from David Gross who wants a moratorium on testing AdS/CFT.
• Best Participant: Lubos Motl, even though off-shell. Probably the first live commentary in the history of physics conferences.
• Best Andy Warhol double: Matthias Staudacher.
  

See also the official summary talk slides and Peter's review of David Gross outlook talk.

It's over now, the string theorists are slowly leaving, the CERN theorists are again the geekiest geeks in town.

Unitarity Rules

Wednesday at Strings'08 was fairly interesting for me, as I'm obviously more attracted by the interface of string and field theory rather than by hard-core strings. In the last few years there has been a lot of commotion in the no man's land between formal string theory/supergravity and the perturbative QCD. This was nicely reviewed by Lance Dixon. This subject is suitable for a 100p review rather than a blog post, but i'll try anyway to sketch the main points.

Perturbative computations in quantum field theory are by far dominated by summing the Feynman diagrams. This is a simple and intuitive method, but it can be cumbersome at times. That is especially true in gauge or gravity theories where the Feynman diagrams propagate many spurious degrees of freedom, and it often happens that the full result is much much simpler than each individual diagram. In such a case, other methods that explore fundamental properties of quantum field theories may prove very handy. Recently, we have been witnessing a come-back of the unitarity based S-matrix approach that was conceived back in the sixties. Geoffrey Chew would be turning in his grave, were he dead.

In fact, we have learned a lot since the summer of love. One thing is the importance of the spinor helicity formalism. For each momentum vector $k_\mu$ of a massless particle one can find corresponding Weyl spinors $\lambda,\bar \lambda$: $k^2$ is the determinant of the matrix $k_\mu (\sigma^\mu)_{ab} $, so that for $k^2 = 0$ the matrix can be written as $\lambda_a \bar \lambda_b$. Similarly, the polarization vectors can be represented using spinors, and one defines the +(-) plus helicity for $\epsilon_\mu (\sigma^\mu)_{ab} \sim \bar \lambda_b (\lambda_b)$. At the end of the day, scattering amplitudes of massless particles can be written as functions of spinor invariants, which reveals unexpected hidden structures. In the Yang-Mills theory, the amplitudes with all helicities of the external gluons being the same, like (++++), are always vanishing. The same is true for the amplitudes with one helicity different than all the others, like (-+++). The simplest non-vanishing amplitude -- the ones with two (+) two (-) helicities -- are called minimal helicity-violating (MHV). There is a compact formula for tree-level MHV amplitudes with an arbitrary number of external gluon legs.

This formalism opened the way for the BCFW recursion relations. To derive these relations, one takes two spinors $\lambda_{1,2}$ corresponding to two external momenta, and continues them analytically to a complex plane, $\lambda_1 \to \lambda_1 + z \lambda_2$, $\bar \lambda_2 \to \bar \lambda_2 - z \bar \lambda_1$. This way, the scattering amplitudes become analytic functions of a fictitious complex variable z. This deformation is designed in such a way that the amplitudes have only simple poles in the z-variable, and the residues of these poles encode information about amplitudes with fewer external legs. Then one can use the usual contour integral methods to relate the amplitude to the residues of its poles, which amounts to relating n-leg amplitudes to those with n-1 legs. This is a powerful method that reduces very complicated multi-legs amplitudes to a sum of simpler (less-leg) ones.
The BCFW relations are being implemented by modern computing tools and Monte Carlos programs.

Yet another interesting development are the use of generalized unitarity relations. Loop amplitudes have branch cuts (in addition to poles), and unitarity strongly constrains what the discontinuity across the branch cut might be. Two-particle cuts are the well-known textbook techniques to relate one-loop amplitudes to tree-level ones. Recently, multi-particle cut techniques have been developed. This jack-the-ripper approach turns out to be useful in reducing general loop amplitudes to simpler building blocks. In particular, arbitrary one-loop amplitudes can be reduced to simple scalar integrals knowns as the box, the triangle and the bubble.


While all the above methods can be applied to the real-life QCD or electroweak theories, they become even more powerful when applied to highly symmetric systems like N=4 super-Yang-Mills or N=8 supergravity. Unitarity is the weapon used on the battlefield of proving perturbative finiteness of N=8 supergravity. Judging from the progress so far, the definitive answer should be known by Strings'09.

It seems that the list of applications is far from being closed. At the same time, there is a feeling that all these surprising results revealed by the unitarity methods are being obtained in a bit roundabout way. There is a fascinating conjecture spelled out in this paper that there exists a dual formulation of quantum field theory where all these surprising properties of scattering amplitudes are realized in a more straightforward way.

Slides here. You can also learn about prof. Mantis Schrimp who was the first to apply the helicity formalism in practice.

Strings ante portas

Tomorrow Strings 2008 kick off here at CERN. The place and the timing of the conference were carefully planned to coincide with the first LHC results that would hint toward string theory. The plan didn't quite work out due to the LHC schedule slip, which means we have to wait one more year for the ultimate confirmation of string theory. The expectation makes it all even more exciting.

The warm-up for Strings 2008 was the Summer Institute on String Phenomenology that has been taking place at CERN TH during the last month. Although I'm usually attracted by wordplay, puns and oxymorons, this time I didn't manage to attend many talks. That's partly due to my summer travelling, and partly due to my summer paresse. Among the few talks I've seen I best remember the one by Cumrun Vafa who talked about F-theory phenomenology. He presented a simple and elegant construction that connects F-theory to reality (that is to the MSSM). Although I wasn't able to grasp all the details, the picture below gives a rough idea:
For detailed experimental predictions, the experimentalists from ATLAS and CMS are encouraged to consult this paper. Although there are no specific predictions for the superparticle spectrum, your perspective may be changed by the fact that the Higgs particle you will discover is in reality a matter curve on Riemann surfaces located at the intersection between the
GUT model seven-brane and additional seven-branes in the full compactification where the U(1) hypercharge flux is non-vanishing. For the neutrino physicists, the important piece of information is that the neutrinos are Dirac or Majorana and their masses are roughly of the order of what is observed. I heard some skeptics saying that back in the old days phenomenology meant a different thing, but such grumbling should not be taken seriously.

Highlights from the conference along with more nasty comments are soon to appear on this blog. Live webcast here or via technically more advanced Lubos' blog.

Un

Since Howard Georgi taught us how to turn anything into unthing, unparticles have quickly spread to all areas of particle physics. This amazing expansion have been so far consistent with the unthropic principle which says that, in the universe that supports intelligent life, unparticles cannot have any useful application. Nothing is sacred these days, and even the Higgs was recently downgraded to the Unhiggs. Yet in spite of my trademark sarcasm, it seems to me that the Unhiggs may violate the unthropic principle and that the whole idea may turn out to be of some use.

In the good old Standard Model, the Higgs particle fulfills multiple tasks. First of all, it condensates to give mass to the W and Z bosons. But this is just a beginning. The presence of the Higgs particle renders the Standard Model well-behaved - *unitary* - at high energies. A massive W boson has three polarization states - two transverse (to the direction of motion), and one longitudinal. It turns out that the scattering amplitude for the longitudinally polarized W's grows with energy, and at some point it would violate general unitarity bounds of quantum field theory. But the diagrams with the Higgs exchange cancel the dangerous terms in the amplitude and the theory recovers the consistent high-energy behavior. In the particle physics jargon, the Higgs unitarizes WW scattering. Finally, the Higgs contributes to electroweak precision observables. The success of the Standard Model in fitting the LEP and Tevatron data relies to a large extent on assuming loop contributions of a fairly light (less than 200 GeV) Higgs particle.

Since the Higgs does his job so well, living without the Higgs particle is difficult. The Higgsless models make a try. They invoke new heavy spin 1 particles to unitarize WW scattering, but they do much worse in electroweak precision tests. It seems that the Unhiggs is a new possibility. Given the dearth of calculable ideas for electroweak symmetry breaking, any new direction is worth looking at.

In a recent paper, David Stancato and John Terning attempted to get W and Z boson masses from a scalar unparticle Higgs condensation. The first step is to construct a gauge invariant action for the Unhiggs. This is actually quite tricky. Usually, making the action gauge invariant amounts to replacing normal derivatives $\pa$ with covariant derivatives $D = \pa - i A$. But the unparticle nature of the Unhiggs implies that the kinetic term is some non-polynomial function $F(\partial^2)$, rather than the simple $\partial^2$, so that the usual procedure does not apply. Yet there is a trick that makes use of non-local objects called the Wilson lines. The final outcome is a complicated, non-local action: whereas in the normal gauge theory there are vertices with only 3 or 4 gauge bosons legs, in the Unhiggs set-up there exist vertices with an arbitrary number of gauge boson legs.

The paper shows that, even though the interactions are weird, the Unhiggs unitarizes WW scattering. It is not clear yet how well it fares with the electroweak precision tests.

The most serious problem with this approach is that it's unclear what would happen if such unthing is discovered at the LHC. If the Higgs particle is discovered, the Nobel Prize will sure go Peter Higgs who predicted a particle, but he obviously cannot be honored for an unparticle. The three possible scenarios are
1) Unpeter Unhiggs gets a Nobel Prize.
2) Peter Higgs gets the Ignoble Prize
3) There is a fatal error and the universe disappears.

We'll see. Or not.

The paper is here, but be warned that it's unpretty technical.