There are rumours appearing here and there about further imminent delays of the LHC start-up. As for the facts, two weeks ago Lyn Evans, who is the LHC project leader, gave a colloquium about the current status of the LHC. He did not mention any delays, but he described in great detail the efforts they are currently undertaking and the problems that have emerged. The video recording of this talk is available here. In particular, at 52:35 Lyn devotes some time to the plug-in modules between magnet interconnects, whose faults spawned the recent rumours. While I personally don't understand why can't they tie up the magnets with strings (or superstrings in the case of superconducting magnets), i guess those more experimentally oriented may get some insight. Anyway, experts advise not to get excited with this particular problem; there will be many others. As Lyn himself put it, at this point we are far less deterministic.

## Monday 24 September 2007

## Saturday 22 September 2007

### Deep Throats and Phase Transitions

Both of my readers have expressed their concern about my lack of activity in the last weeks. OK, let's say i wasn't in mood and go back to business.

Last week John March-Russell gave a seminar entitled Throats with Faster Holographic Phase Transitions. This sounds very encouraging to stay for another coffee in the cafeteria. This time, however, the first intuition would be wrong, as behind this awkward title hides an interesting and less studied piece of physics.

The story is about the Randall-Sundrum model (RS1, to be precise): five-dimensional theory in approximately AdS5 space cut off by the Planck and the TeV branes. The question is what happens with this set-up at high temperatures. There is a point of view from which the high-temperature phase can be simply understood. Here at CERN the local folks believe that the Randall-Sundrum set-up is a dual description of a normal (though strongly coupled) gauge theory in four dimensions. Therefore at high temperatures such phenomena as deconfinement or the emergence of a gluon plasma should be expected. How this phase transition manifests itself in the 5D description?

This last question was studied several years ago in a paper by Creminelli et al based on earlier results by Witten. It turns out that one can write down another solution of the Einstein equations that describes a black hole in the Ads5 space. The black hole solution is a dual description of the high-temperature deconfined phase: the TeV brane (whose presence implies the existence of a mass gap in the low-temperature phase) is hidden behind the black hole horizon.

Which of the two solutions dominates, that is to say, which one gives the dominant contribution to the path integral depends on the free energy F = E- T S. One can calculate that at zero temperature the RS1 solution has lower free energy. But the black hole solution has entropy associated with the black hole horizon and its free energy ends up being lower at high enough temperature. This black hole solution effectively describes a high-temperature expanding universe filled with a hot gluon plasma. As the temperature goes down to the critical value, the RS1 solution with a TeV brane becomes energetically more favorable and a first order phase transition occurs.

Creminelli et al computed the critical temperature at which free energies of the two phases are equal. They also estimated the rate of phase transition between the black hole and the RS1 phases. It turns out that, with the assumption they made about the mechanism stabilizing the fifth dimension, the rate is too low so that the phase transition could never be completed. The universe expands too fast and, although bubbles of the RS1 phase do form, they do not collide. One ends up with an empty ever-inflating universe. From this analysis it seems that, if RS1 is to describe the real world, the temperature of the universe should never exceed the critical one. Although this assumption does not contradict any observations, it makes life more problematic (how to incorporate inflation, bariogenesis...)

According to John, the problem with too slow phase transitions is not general but specific to the stabilization mechanism assumed by Creminelli et al. In his recent paper, John studied a modified version of RS1 - a string-inspired set-up called the Klebanov-Tseytlin throat. From the picture it is obvious that the Klebanov-Tseytlin throat is dual to a punctured condom. John found that in this modifed set-up the phase transition is fast enough to complete. The key to the success seems to be the fact that the different stabilization mechanism results

in a strong breaking of conformal symmetry in IR.

So much for now, more details in the paper. I think this subject is worth knowing about. It connects various areas of physics and cosmology and does not seem to be fully explored yet. First order phase transitions, like the one in RS1, may also leave observable imprints in the gravity waves spectrum, as discussed here.

Slides available.

Last week John March-Russell gave a seminar entitled Throats with Faster Holographic Phase Transitions. This sounds very encouraging to stay for another coffee in the cafeteria. This time, however, the first intuition would be wrong, as behind this awkward title hides an interesting and less studied piece of physics.

The story is about the Randall-Sundrum model (RS1, to be precise): five-dimensional theory in approximately AdS5 space cut off by the Planck and the TeV branes. The question is what happens with this set-up at high temperatures. There is a point of view from which the high-temperature phase can be simply understood. Here at CERN the local folks believe that the Randall-Sundrum set-up is a dual description of a normal (though strongly coupled) gauge theory in four dimensions. Therefore at high temperatures such phenomena as deconfinement or the emergence of a gluon plasma should be expected. How this phase transition manifests itself in the 5D description?

This last question was studied several years ago in a paper by Creminelli et al based on earlier results by Witten. It turns out that one can write down another solution of the Einstein equations that describes a black hole in the Ads5 space. The black hole solution is a dual description of the high-temperature deconfined phase: the TeV brane (whose presence implies the existence of a mass gap in the low-temperature phase) is hidden behind the black hole horizon.

Which of the two solutions dominates, that is to say, which one gives the dominant contribution to the path integral depends on the free energy F = E- T S. One can calculate that at zero temperature the RS1 solution has lower free energy. But the black hole solution has entropy associated with the black hole horizon and its free energy ends up being lower at high enough temperature. This black hole solution effectively describes a high-temperature expanding universe filled with a hot gluon plasma. As the temperature goes down to the critical value, the RS1 solution with a TeV brane becomes energetically more favorable and a first order phase transition occurs.

Creminelli et al computed the critical temperature at which free energies of the two phases are equal. They also estimated the rate of phase transition between the black hole and the RS1 phases. It turns out that, with the assumption they made about the mechanism stabilizing the fifth dimension, the rate is too low so that the phase transition could never be completed. The universe expands too fast and, although bubbles of the RS1 phase do form, they do not collide. One ends up with an empty ever-inflating universe. From this analysis it seems that, if RS1 is to describe the real world, the temperature of the universe should never exceed the critical one. Although this assumption does not contradict any observations, it makes life more problematic (how to incorporate inflation, bariogenesis...)

According to John, the problem with too slow phase transitions is not general but specific to the stabilization mechanism assumed by Creminelli et al. In his recent paper, John studied a modified version of RS1 - a string-inspired set-up called the Klebanov-Tseytlin throat. From the picture it is obvious that the Klebanov-Tseytlin throat is dual to a punctured condom. John found that in this modifed set-up the phase transition is fast enough to complete. The key to the success seems to be the fact that the different stabilization mechanism results

in a strong breaking of conformal symmetry in IR.

So much for now, more details in the paper. I think this subject is worth knowing about. It connects various areas of physics and cosmology and does not seem to be fully explored yet. First order phase transitions, like the one in RS1, may also leave observable imprints in the gravity waves spectrum, as discussed here.

Slides available.

## Monday 3 September 2007

### Drowning the Hierarchy Problem

For a change, the third week of the New Physics workshop turned out to be very interesting. In this post I tell you about Gia Dvali and his brand new idea of solving the hierarchy problem. Several other talks last week deserves attention and I hope to find more time to write about it.

Gia first argued for the following result. Suppose there exists N particle species whose mass is of order M. Further suppose that these species transform under exact gauged discrete symmetries. Then there is a lower bound on the Planck scale:

The bound has several interesting consequences. One is that it can be used to drown the hierarchy problem in the multitude of new particles. Just assume there exists something like 10^32 new charged particle species at the TeV scale. If that is the case, the Planck scale cannot help being 16 orders of magnitude higher than the TeV scale. For consistency, gravity must somehow become strongly interacting at the TeV scale, much as in the ADD or RS model, so that the perturbative contributions to the Higgs mass are cut off at the TeV scale. Thus, in Gia's scenario the LHC should also observe the signatures of strongly interacting gravity.

You might say this sounds crazy...and certainly it does. But, in fact, the idea is not more crazy than the large extra dimensions of the ADD model. The latter is also an example of many-species solution to the hierarchy problem. In that case there are also 10^32 degrees of freedom - the Kaluza-Klein modes of the graviton, which make gravity strongly interacting at TeV. The difference is that most of the new particles is much lighter than TeV, which creates all sorts of cosmological and astrophysical problems. In the present case these problems can be more readily circumvented.

Transparencies available on the workshop page.

Gia first argued for the following result. Suppose there exists N particle species whose mass is of order M. Further suppose that these species transform under exact gauged discrete symmetries. Then there is a lower bound on the Planck scale:

$M_p > N^{1/2} M$

The proof goes via black holes. As argued in the old paper by Krauss and Wilczek, gauged discrete symmetries should be respected by quantum gravity. Therefore, if we make a black hole out of particles charged under a gauged discrete symmetry, the total charge will be conserved. For example, take a very large number N of particles, each carrying a separate Z2 charge. Form a black hole using an odd number of particles from each species, so that the black hole carries a Z2^N charge. Then wait and see what happens. According to Hawking, the black hole should evaporate. But it cannot emit the charged particles and reduce its charge before its temperature becomes of order M. The relation between the black hole temperature and mass goes like $T \sim M_p^2/M_{BH}$. Thus, by the time the charge starts to be emitted, the black hole mass is reduced to $M_{BH} = M_p^2/M$. To get rid of all its charge the black hole must emit at least N particles of mass M, so its mass at this point must satisfy $M_{BH} > N M$. From this you easily obtain Gia's bound.The bound has several interesting consequences. One is that it can be used to drown the hierarchy problem in the multitude of new particles. Just assume there exists something like 10^32 new charged particle species at the TeV scale. If that is the case, the Planck scale cannot help being 16 orders of magnitude higher than the TeV scale. For consistency, gravity must somehow become strongly interacting at the TeV scale, much as in the ADD or RS model, so that the perturbative contributions to the Higgs mass are cut off at the TeV scale. Thus, in Gia's scenario the LHC should also observe the signatures of strongly interacting gravity.

You might say this sounds crazy...and certainly it does. But, in fact, the idea is not more crazy than the large extra dimensions of the ADD model. The latter is also an example of many-species solution to the hierarchy problem. In that case there are also 10^32 degrees of freedom - the Kaluza-Klein modes of the graviton, which make gravity strongly interacting at TeV. The difference is that most of the new particles is much lighter than TeV, which creates all sorts of cosmological and astrophysical problems. In the present case these problems can be more readily circumvented.

Transparencies available on the workshop page.

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