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Kaminski, Matthias (2008): Holographic quark gluon plasma with flavor. Dissertation, LMU München: Faculty of Physics
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Abstract

In this thesis we explore the effects of chemical potentials or charge densities inside a thermal plasma, which is governed by a strongly coupled gauge theory. Since perturbative methods in general fail in this regime, we make use of the AdS/CFT correspondence which originates from string theory. AdS/CFT is a gauge/gravity duality (also called holography), which we utilize here to translate perturbative gravity calculations into results in a gauge theory at strong coupling. As a model theory for Quantum-Chromo-Dynamics (QCD), we investigate N=4 Super-Yang-Mills theory in four space-time dimensions. This theory is coupled to fundamental hypermultiplets of N=2 Super-Yang-Mills theory. In spite of being quite different from QCD this model succeeds in describing many of the phenomena qualitatively, which are present in the strong interaction. Thus, the effects discovered in this thesis may also be taken as predictions for heavy ion collisions at the RHIC collider in Brookhaven or the LHC in Geneva. In particular we successively study the introduction of baryon charge, isospin charge and finally both charges (or chemical potentials) simultaneously. We examine the thermodynamics of the strongly coupled plasma. Phase diagrams are given for the canonical and grandcanonical ensemble. Furthermore, we compute the most important thermodynamical quantities as functions of temperature and charge densities~(or chemical potentials): the free energy, grandcanonical potential, internal energy and entropy. Narrow resonances which we observe in the flavor current spectral functions follow the (holographically found) vector meson mass formula at low temperature. Increasing the temperature the meson masses first decrease in order to turn around at some temperature and then increase as the high-temperature regime is entered. While the narrow resonances at low temperatures can be interpreted as stable mesonic quasi-particles, the resonances in the high-temperature regime are very broad. We discuss these two different temperature-regimes and the physical relevance of the discovered turning point that connects them. Moreover, we find that flavor currents with isospin structure in a plasma at finite isospin density show a triplet splitting of the resonances in the spectral functions. Our analytical calculations confirm this triplet splitting also for the diffusion pole, which is holographically identified with the lowest lying quasinormal frequency. We discuss the non-vanishing quark condensate. Furthermore, the baryon diffusion coefficient depends non-trivially on both: baryon and isospin density. Guided by discontinuities in the condensate and densities, we discover a phase transition resembling the one found in the case of 2-flavor QCD. Finally, we extend our hydrodynamic considerations to the diffusion of charmonium at weak and strong coupling. As expected, the ratio of the diffusion coefficient to the meson mass shift at strong coupling is significantly smaller than the weak coupling result. This result is reminiscent of the result for the viscosity to entropy density ratio, which is significantly smaller at strong coupling compared to its value at weak coupling.