Holographic quark gluon plasma with flavor

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.