### GRG18 5c

There were a number of interesting talks on Friday last week. In the morning we heard from Rob Myers on Quark Soup at RHIC. The header slide included this cool image. Myers than made a quip about a string theorist talking about nuclear physics at a gravity meeting, dispelling the fears ignited by the talk title that grand claims would be made for string theory. On the other hand, the introduction included a mention of both the 2004 Nobel prize and the Clay Institute Yang-Mills problem, neither of which seem particularly relevant except in the context of a potential leap in our understanding of QCD. Ashtekar asked the inevitable question at the end of the talk, but Myers simply admitted that he didn't really know what it all meant.

This story is about the use of 5d AdS gravity to compute in N=4 SUSY Yang-Mills, which is taken to be close enough to real QCD in certain regimes of the temperature density phase diagram. RHIC data indicates that high temperature (just above $T_{c}$) quark-gluon plasmas display fluid like behaviour. This hydrodynamic model correctly predicts the elliptic flow. A necessary assumption is that the shear viscosity $\eta$ is small and it was found theoretically that

$\frac{\eta}{S} \simeq 1$

where $S$ is entropy density. This suggests the need for a non-perturbative approach. For $L$ a length scale in the AdS metric, it turns out that the entropy density is given by

$S = \frac{1}{4 G_{5}} \frac{r_{0}^{3}}{L^{3}} = 0.75 S_{free}$

where $r_{0}$ is at the AdS horizon. The 0.75 factor transfers to the observed 0.75 value for normalised energy density, characteristic of fluids. This is thought to be a universal characteristic of gauge theories, in which case the string techniques are computationally impressive but devoid of new physical content. Under AdS/CFT, fluctuations in gravitational horizons become deviations from equilibrium in plasmas. The $\frac{\eta}{S}$ ratio is stable under higher order corrections.

This story is about the use of 5d AdS gravity to compute in N=4 SUSY Yang-Mills, which is taken to be close enough to real QCD in certain regimes of the temperature density phase diagram. RHIC data indicates that high temperature (just above $T_{c}$) quark-gluon plasmas display fluid like behaviour. This hydrodynamic model correctly predicts the elliptic flow. A necessary assumption is that the shear viscosity $\eta$ is small and it was found theoretically that

$\frac{\eta}{S} \simeq 1$

where $S$ is entropy density. This suggests the need for a non-perturbative approach. For $L$ a length scale in the AdS metric, it turns out that the entropy density is given by

$S = \frac{1}{4 G_{5}} \frac{r_{0}^{3}}{L^{3}} = 0.75 S_{free}$

where $r_{0}$ is at the AdS horizon. The 0.75 factor transfers to the observed 0.75 value for normalised energy density, characteristic of fluids. This is thought to be a universal characteristic of gauge theories, in which case the string techniques are computationally impressive but devoid of new physical content. Under AdS/CFT, fluctuations in gravitational horizons become deviations from equilibrium in plasmas. The $\frac{\eta}{S}$ ratio is stable under higher order corrections.

## 2 Comments:

It's interesting how the potential energy of the various (strong, weak, electromagnetic) fields varies quantitatively as a function of distance from particle cores (not just as a function of collision energy).

The principle of conservation of energy then makes predictions for the variations of different SM charges with distance.

I.e., the strong (QCD) force peaks at a particular distance.

At longer distances, it falls exponentially because of the limited range of the massive pions which mediate it.

At much shorter distances (where it is mediated by gluons) it also decreases.

How does energy conservation apply to such 'running couplings' or variations in effective charge with energy and distance?

This whole way of thinking objectively and physically is ignored completely by the standard model QFT. As the electric force increases at shorter distance, the QCD force falls off; the total potential energy is constant; the polarized vacuum creates QCD by shielding electric force. This physical mechanism makes falsifiable predictions about how forces behave at high energy, so it can be checked experimentally.

It sounds like the fascinating conference I was expecting. Too bad the business in Chicago came up, it would be great to be in 2 places at once. Betwseen the two of us we can be both places.

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