Aspects of transport in strongly correlated systems with gravity duals
In this thesis we consider various applications the gauge/gravity duality to study transport in strongly coupled systems. The main content is organized in three parts. In the first part we investigate the interrelation between dimensionality and strength of interactions. It is known that the dynamics of systems in Condensed Matter and General Relativity simplify for high dimensionality. Therefore, in this limit of large dimensionality, analytic results are usually possible. We study the dependence of the conductivity and the entanglement entropy on the space-time dimensionality in two different models of holographic superconductors: one dual to a quantum critical point with spontaneous symmetry breaking, and the other modelled by a charged scalar that condenses at a sufficiently low temperature in the presence of a Maxwell field. In the large dimensionality limit we obtain explicit analytical results for the conductivity at zero temperature and the entanglement entropy. Our results suggest that, as dimensionality increases, the condensate interactions become weaker. In the second part we first investigate the Drude weight and the related Mazur-Suzuki (MS) bound in a broad variety of strongly coupled field theories with a gravity dual at nonzero temperature and chemical potential. We show that the MS bound, which in the context of Condensed Matter provides information on the integrability of the theory, is saturated in Einstein-Maxwell-dilaton (EMd) and R-charged backgrounds. We then explore EMd theories with U(1) spontaneous symmetry breaking, and gravity duals of non-relativistic field theories, in which the MS bound is not saturated. Finally, we study the effect of a weak breaking of translational symmetry and we show that the MS bound sets a lower bound on the DC conductivity for a given scattering time. In the last part, we study asymptotically anti de Sitter Brans-Dicke (BD) backgrounds as effective models of metals with a varying coupling constant. We show that, for translational invariant backgrounds, the zero-frequency conductivity (dc conductivity) deviates from the universal result of EMd models. Once translational symmetry is broken, the shear viscosity to entropy ratio is always lower than the Kovtun-Son-Starinets bound, in line with other gravity backgrounds with momentum relaxation. In the BD models studied, we observed insulating like features in the dc conductivity. However, the module and argument of the optical conductivity at intermediate frequencies are not consistent with cuprates experimental results, even assuming several channel of momentum relaxation. We have also included the research carried out in the first year of the PhD as appendices. The topics studied in these appendices lie outside the main framework of this thesis.
AdS/CFT, Holography, Strongly correlated systems, Condensed Matter
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