Holographic approaches to strongly-interacting systems

In this thesis, we investigate some applications of the gauge/string duality to strongly-coupled quantum field theories. After a brief review of the duality and the main entries of the holographic dictionary, we explore the asymptotic nature of the gradient expansion for Bjorken flow using the fluid/gravity correspondence. We link the divergence of the series to the presence of non-perturbative quasi-normal modes and construct the hydrodynamic attractor, using Borel-Padé summation techniques. We find that different initial conditions hydrodynamise, at large values of the pressure anisotropy, before the plasma has had time to reach thermal equilibrium. We then explore the transport properties of zero sound modes in a family of holographic strange metals. We find sound modes with speed given by the conformal value and attenuation constant given by hydrodynamic form at arbitrarily low temperatures, even outside of the usual hydrodynamic regime. The sound attenuation constant as a function of temperature qualitatively resembles that of a Landau Fermi liquid zero sound, including a maximum between the collisionless and the hydrodynamic regimes. In order to get insight into these low temperature sound modes, we introduce a new quantity called ''entanglement density", which we study holographically for a range of systems and relevant deformations. We conclude that its asymptotic nature is linked to the area theorem of entanglement, and that it can be used to classify states of quantum matter according to their long-range entanglement and the violation of the area theorem.