Anomaly induced transport coefficients: from weak to strong coupling

Resumo

The description of the high energy physics and the interactions between elementary particles are based on gauge theories. The Standard Model and in particular QCD are examples of gauge theories. Some of the most important features of non-Abelian gauge theories and in consequence of high energy physics are not accessible through perturbation theory. Confinement and chiral symmetry breaking are examples of phenomena which need more sophisticated techniques to be explained. During the seventies [1] G. ¿t Hooft realized that the perturbative series of gauge theories can be rearranged in terms of the rank of the gauge group Nc and the effective coupling constant lt = g2Y MNc called ¿t Hooft coupling. In the limit Nc !¥ the series looks like an expansion summing over 2D surfaces, that suggested that gauge theories had an effective description in terms of a string theory model. It wasn¿t until 1997 almost twenty years later that the ¿t Hooft ideas were realized when J. Maldacena published his very famous paper [2] which revolutionized the fields of Strings and Quantum Field Theory. This paper was the starting point of the construction of the holographic principle through the introduction of the AdS=CFT correspondence which tells us that the N = 4 SU(Nc) Super-Yang-Mills (SYM) theory in 4-dimensions is dual to the type IIB string theory on AdS5S5. This correspondence relates the string theory coupling constant gs with 1=Nc and the radius of the AdS space with the t¿ Hooft coupling. Beside the t¿ Hooft¿s ideas this correspondence is also a realization of the holographic principle which says that a quantum gravity theory should be described with the degrees of freedom living at the boundary of the space. In this case the space of quantum gravity is the 10-dimensional space of the string theory and the boundary is the 4-dimensional conformal boundary associated to that space (AdS5S5). The degrees of freedom of the theory at the boundary are precisely the ones of the SYM theory. In fact, at present time AdS=CFT not only refers to Maldacena¿s duality but a framework of many dualities realizing the holographic principle. The really useful fact of this duality is its weak/strong character; from the view point of the field theory the weakly coupled situation is described by the four dimensional perturbative gauge theory but the strong coupling scenario is described by string theory in ten dimensions1. An interesting application of the AdS=CFT duality is given by asymptotically AdS black holes. According to the holographic dictionary a black hole embedded in an AdS space-time is dual to a thermal state in the field theory side. One of the most important and known results of holography, at least from a phenomenological point of view is the very small lower bound in the ratio of shear viscosity to entropy density in all the Holographic plasmas which are dual to an Einstein-Hilbert gravity h=s > ¯h=(4pkB) [3] 2. This result had a big impact because the measure in the experiment RHIC of that ratio for the Quark-Gluon Plasma (QGP) was 2:5 ¯h=(4pkB), suggesting that the plasma is in a strongly coupled regime because the prediction for h=s coming from weak coupling is in contrast very large. The indications of the production of a quantum liquid in a strongly coupled regime at the experiments RHIC and more recently at the LHC, pushed forward AdS=CFT as a very promising framework to construct phenomenological models to try to understand and predict the behaviour of the QGP.