An inspiring paper

These days I am closed at home due to the effects of flu. When such bad symptoms started to relax I was able to think about physics again.  So, reading the daily from arxiv today I have uncovered a truly inspiring paper from Antal Jakovac a and Daniel Nogradi (see here). This paper treats a very interesting problem about quark-gluon plasma. This state was observed at RHIC at Brookhaven. Successful hydrodynamical models permit to obtain values of physical quantities, like shear viscosity, that could be in principle computed from QCD. The importance of shear viscosity relies on the existence of an important prediction from AdS/CFT symmetry claiming that the ratio between this quantity and entropy density can be at least $1/4\pi$. If this lower bound would be proved true we will get an important experimental verification for AdS/CFT conjecture.

Jakovac and Nogradi exploit the computation of this ratio for SU(N) Yang-Mills theory. Their approach is quite successful as their able to show that the value they obtain is still consistent with the lower bound as they have serious difficulties to evaluate the error. But what really matters here is the procedure these authors adopt to reach their aim making this a quite simple alley to pursuit when the solution of Yang-Mills theory in infrared is acquired. The central point is again the gluon propagator. These authors assume simply the very existence of a mass gap taking for the propagator something like $e^{-\sigma\tau}$ in Euclidean time. Of course, $\sigma$ is the glueball mass. This is a too simplified assumption as we know that the gluon propagator is somewhat more complicated and a full spectrum of glueballs does exist that can contribute to this computation (see my post and my paper).

So, I spent my day to extend the computations of these authors to a more realistic gluon propagator.  Indeed, with my gluon propagator there is no need of one-loop computations as the identity at 0-loop $G_T=G_0$ does not hold true anymore for a non-trivial spectrum and one has immediately an expression for the shear viscosity. I hope to give some more results in the near future.

2 Responses to An inspiring paper

1. Trent says:

There is a second version out with a slightly modified end result for eta / s, apparently the large N limit of the previous formula was not correct. The new formula has the expected O(N^2) scaling.

• mfrasca says:

Thanks a lot for pointing me this out. I will take time in the week-end to read it.

Marco

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