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We provide a framework for calculating holographic Green's functions from general bilinear actions and fields obeying coupled differential equations in the bulk. The matrix-valued spectral function is shown to be independent of the radial bulk coordinate. Applying this framework we improve the analysis of fluctuations in the D3/D7 system at finite baryon density, where the longitudinal perturbations of the world-volume gauge field couple to the scalar fluctuations of the brane embedding. We compute the spectral function and show how its properties are related to the quasinormal mode spectrum. We study the crossover from the hydrodynamic diffusive to the reactive regime and the movement of quasinormal modes as functions of temperature and density. We also compute their dispersion relations and find that they asymptote to the lightcone for large momenta.

We study the holographic dual model of quenched flavors immersed in a quark-gluon plasma with massless dynamical quarks in the Veneziano limit. This is modeled by embedding a probe D7 brane in a background where the backreaction of massless D7 branes has been taken into account. The background, and hence the effects, are perturbative in the Veneziano parameter N f /N c , therefore giving small shifts of all magnitudes like the constituent mass, the quark condensate, and several transport coefficients. We provide qualitative results for the effect of flavor degrees of freedom on the probes. For example, the meson melting temperature is enhanced, while the screening length is diminished. The drag force is also enhanced.

We compute the shear viscosity in the supersymmetric Yang-Mills theory dual to the STU background. This is an example of thermal gauge theory with a nonzero chemical potential. The quotient of the shear viscosity over the entropy density exhibits no deviation from the well known result η/s = 1/4π.

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