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.