Generalisations of holographic hydrodynamics: anomalous transport & fermionic universality

In the present thesis we study properties of strongly coupled hydrodynamic theories which may be described in terms of a dual higher dimensional gravitational system. Particular attention is given to the computation of physical quantities like the theories’ viscosities and diffusion constants. These are analysed with regard to the question of whether they follow generally applicable, universal laws which may be derived from the description in terms of a gravitational theory. The theoretical foundation for this is laid by the duality between conformal quantum field theories in Minkowski space and higher-dimensional string theories on Anti-de Sitter space, the AdS/CFT correspondence. A particularly interesting simplification is given by the limit of strong coupling and large number of degrees of freedom of the conformal field theory in which the dual description reduces to a classical theory of gravity on AdS space. By using a perturbative treatment of fluctuations of the gravitational theory’s black hole solutions one may describe universal hydrodynamic properties of the strongly coupled field theory. One of the main results within this area of research is the proof that fluids which may be described by a simple dual gravitational theory with unbroken rotational invariance possess a universal ratio of shear viscosity and entropy density. Astonishingly, this ratio parametrically agrees with the value measured for the strongly-coupled quark gluon plasma, although a direct treatment of this QCD phase is at present not available. In the following work we describe the construction of a similar, universal relation. In the hydrodynamic description of supersymmetric field theories there exists a further diffusion constant which, similarly to the shear viscosity, appears in the traceless part of the constitutive relation of the supersymmetry current. We compute this constant in supersymmetric theories of arbitrary dimension via different independent calculations. For doing so we look at a generic supergravity theory as the gravitational dual. The equation of motion of a gravitino, which is the dual field to the supersymmetry current, is solved in a black hole background and allows for the computation of retarded Green’s functions of the field theory’s supersymmetry current. This has a pole which describes the characteristic sound dispersion relation of the phonino, the Goldstone fermion of spontaneously broken supersymmetry due to finite temperature. In this dispersion relation we find the aforementioned diffusion constant which we also obtain directly from the correlator via a new Kubo formula. The main result of this project is the establishment of a relation of the supersound diffusion constant and a universally applicable absorption cross section on the dual gravitational side which describes the absorption of spinors by a black hole. A further important development is the discovery of a new transport coefficient which describes the observable current that is induced by the vorticity of a fluid. This illustrates the classical manifestation of a quantum mechanical effect which appears when the underlying microscopic theory possesses a quantum mechanical chiral anomaly. We investigate this effect within a theoretical framework which unifies several different approaches at the interplay of hydrodynamics and gravitational physics. We effectively describe rotating D3-branes as asymptotically flat generalisations of fivedimensional AdS Reissner-Nordstrom black holes. The fluctuations of this background describe an effective hydrodynamical theory on a surface at a finite distance from the black hole’s singularity, on which the fluctuations satisfy Dirichlet boundary conditions. This approach allows us to study the mentioned quantum effect not only at the boundary of AdS space, but also at the black hole’s horizon, at a surface in between at finite radius, or even in asymptotically flat space.