### Programme Overview

Quantum Chromo Dynamics (QCD) is the theory of the strong nuclear interactions. It is an example of a non-abelian gauge theory. Such theories constitute the fundamental paradigm of modern high energy physics. Although some thirty years have passed by since their invention they are still far from being understood satisfactorily. In particular phenomena such as confinement and chiral symmetry breaking are still lacking complete explanations.QCD is an asymptotically free theory, i.e. its coupling constant runs to smaller and smaller values at high energy. Very early on this has led to the suggestion that confinement ceases to be effective at very high temperature (or density) and that the theory goes over into a deconfined phase: the quark-gluon plasma. An experimental programme has been set up at the Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Laboratory in the USA to establish and study the phase transition towards the Quark Gluon plasma in heavy ion collision.

From next year on, the LHC collider at CERN, Geneva, will also have an ultrarelativistic heavy-ion program which will cover even higher energies and temperatures. The existing experimental results from RHIC indicate that the newly created state of matter in these heavy ion collisions does indeed have properties that are consistent with a deconfined phase of QCD. Somewhat surprisingly it turned out, however, that the new state of matter created in RHIC collisions does not behave as a weakly interacting gas of quarks and gluons but rather as a liquid showing significant collective flow phenomena. Of particular interest is the so called elliptic flow that appears in non-central heavy ion collisions. The elliptic flow data indicate that the liquid of nuclear matter has an extraordinarily low viscosity. It even appears to be the most perfect fluid observed in nature so far, having a specific viscosity (viscosity to entropy ratio) at least an order of magnitude smaller than that of any previously observed liquid.

The temperatures reached in the heavy ion collisions at RHIC are around 350MeV, which is about twice the critical temperature of QCD. At these temperature QCD is still very strongly interacting and therefore the new state of matter created in RHIC collisions has been named the strongly coupled quark gluon plasma (sQGP). The strong coupling behaviour makes perturbative field theoretical approaches to explain the properties of the quark-gluon plasma in this temperature range a nearly impossible task. Since the lifetime of the QGP in heavy ion collisions is very short (of the order of 10 fm/c), time evolution and out-of-equilibrium physics play a central role. Lattice QCD which can in principle address the strong coupling regime faces significant obstacles when trying to apply it to real time phenomena, such as the calculation of transport coefficients as the viscosity.

During the last years a radical new approach to model the strongly interacting QGP has been proposed and developed. It relies on the by now well-tested duality between the maximally supersymmetric (N=4) gauge theory in four dimensions and type IIB string theory on anti-de Sitter space, the so called AdS/CFT correspondence first formulated by Maldacena in 1997. In this framework, the (conformal) boundary values of the five-dimensional supergravity fields provide the sources for the gauge invariant operators of the four dimensional gauge theory, which thus can be thought of as living on the conformal boundary of AdS, hence the terms anti-de Sitter holography and holographic gauge theories. As observed early on by Witten, this correspondence can be generalized to finite temperature, where the deconfinement phase transition in the gauge theory is mapped to the Hawking-Page phase transition of black hole formation in five-dimensional anti-de Sitter space. This approach has by now been greatly generalized to gauge theories which include matter in fundamental representations, whose dual versions involve space-time filling D-brane solutions in the supergravity setting and which generalizes the duality to non-conformal gauge theories where part (or all) of the N=4 supersymmetry is broken.

One of the initial highlights of the holographic approach has been the calculation of the shear viscosity, which turned out to take a universal value in every holographic gauge theory. Numerically this is a very small value, much smaller than results fromperturbative QCD and unlike the latter apparently consistent with the experimental data from RHIC. In fact it has been conjectured that the above value represents a universal lower quantum bound for the specific viscosity of any liquid in nature! Other examples for the application of the AdS/CFT correspondence to the strongly coupled QGP include the calculation of the energy loss rate of a heavy quark moving in the medium, the jet-quenching parameter using light like Wilson loops, all giving better order-of-magnitude estimates than perturbative field theory calculations.

These developments have stimulated enormous interest and activity in the recent years. One aspect of this line of research needs special emphasis: it has instigated extraordinary fruitful interaction, communication and collaboration between two different scientific communities: the community of finite temperature field theorists and string theorists.

The programme shall bring together leading researcher from both of those fields to intensify and deepen this already fruitful cross-fertilizing of ideas coming partially from string theory and partially from finite temperature field theory. In addition an attempt shall be made to involve another scientific community: that of researcher in black hole physics and numerical relativity. Indeed many topics of black hole physics play a crucial role in the AdS/CFT application to the QGP: the interpretation of the black hole entropy as the entropy of the field theory, the spectrum of black hole quasinormal modes to mention only two and we expect that other topics such as critical collapse or dynamical horizons will play an important role in the near future.

The ESI programme shall therefore make an effort to reach out to the community of researchers in black hole physics and numerical relativity. Leading scientists in this fields shall be invited to lecture on their research and to participate actively during the programme