# Quark-Gluon Plasma and String Theory

by Pavel Kovtun

What does quark-gluon plasma have to do with black holes? The question is actually not so silly as it sounds. In fact, black holes constitute an essential part of the theoretical apparatus which is used to understand thermal properties of various strongly interacting QCD-like systems. The whole setup goes by the name of "AdS/CFT correspondence", and has generated interest from both QCD and black hole theorists. The number of recent papers trying to connect black holes to RHIC physics measures in hundreds, RHIC theorists are invited to major string theory conferences, and string theorists are invited to major heavy ion meetings. What is this all about?

When the temperature of the quark-gluon plasma is of the order of couple hundred MeV (the temperature range relevant for RHIC), then the quark-gluon plasma is not a collection of weakly interacting quarks and gluons. It is not even a collection of strongly interacting quarks and gluons. Rather, it is a "hot soup" of strongly fluctuating quantum fields, in which particle-like "quarks" and "gluons" cease to exist. For a theorist, it is a mess.

This is where the AdS/CFT correspondence (see
hep-th/9905111
for a review) has the potential to help. Put simply, the
correspondence states that when the quantum fluctuations are
strong, a QCD-like field theory is just string theory in
disguise. According to the correspondence, *string theory
and QCD-like field theory are simply two different
representations of the same thing --- just like position and
momentum representations in quantum mechanics are simply two
different views of exactly the same physics.* The string
description of the QCD-like worlds is tractable when quantum
fluctuations are strong, precisely when conventional QCD methods
break down. This is why one can see RHIC theorists working on
5-dimensional strings, and string theorists arguing about jet
quenching.

So far the approach has produced interesting results on thermodynamics, transport coefficients (for a review see arXiv:0704.0240), real-time spectral functions, parton energy loss, and real-time evolution of the strongly coupled medium. The method allows for first-principles calculations of various interesting quantities, such as the real space picture of the energy deposited by a heavy quark in the medium, reported recently in arXiv:0706.0368 (see figure).

Probably the most intriguing result that emerged from the AdS/CFT approach is the universal prediction of small viscosity at strong coupling. It turns out that kinematic viscosity is exactly the same (and very small) for an infinite class of QCD-like theories! In terms of numbers, AdS/CFT predicts for the ratio of shear viscosity to entropy density η/s ~ 1/4π ~ 0.08 (hep-th/0405231), while an extrapolation of the perturbative QCD prediction gives approximately η/s > 1.6 (nucl-th/0604032). What exactly the viscosity of the RHIC matter is still remains to be seen, but it is worth emphasizing that AdS/CFT deals with QCD-like matter which is at least 20 times more ideal than perturbative QCD in terms of fluidity.

The advantage of the AdS/CFT approach is that it allows one to perform robust real-time calculations when interactions are strong. The disadvantage is that the QCD-like theories which are tractable by AdS/CFT are not the actual QCD: they contain extra particles in addition to quarks and gluons. This however should not make one discouraged, given that such a powerful non- perturbative approach as lattice QCD was not able to simulate the actual QCD for about 30 years (unphysical quark masses, partial quenching). It seems reasonable to give AdS/CFT some time and see where it takes us.

An interesting part of the whole program is that it brings together theorists from such different communities as string theory and RHIC physics who talk to each other, learn from each other, and can better appreciate each other's field. So if you see a string theorist somewhere on the BNL grounds, don't pass by --- he (or she) may be willing to convert to become a nuclear physicist.

For further details about the AdS/CFT approach to RHIC physics, see online talks at the recent Perimeter Institute workshop "Exotic states of hot and dense matter and their dual description."