Gauge/gravity dualities, Navier-Stokes equations with soft-hair, and Dirac fluids

Abstract

This project develops and implements theoretical and phenomenological aspects of AdS/CFT and AdS/CMT correspondences. Generalized black branes will be studied in AdS4 and AdS5, and the respective corrections to the Navier-Stokes equations in dual field theory, containing soft hair, will be derived, with additional diffusion and coupling terms with the Ricci curvature, with effective viscosity and induced metric with BMS symmetry. Classical and quantum effects will be studied, from the theory of hydrodynamic transport in metals at finite temperature and chemical potential at the boundary. The spectral functions will be computed, as well as the transport and response coefficients, and their consequences will be explored in the emergent Fermi liquids approach. Dirac's fluids will be then studied in terms of a renormalizable gravitational action with higher-order curvature terms. We will improve the relativistic non-perturbative hydrodynamic theory of electron transport in the Dirac fluid, in strange metals, and graphene. The Dirac fluid instabilities in graphene will be investigated, as well as its relationship with vortex formation. We will analyze the instability of AdS and turbulence phenomena in the gravitational collapse of a scalar field, also in the context of generalized black branes in AdS, as well as instabilities and turbulence phenomena that emerge in the context of the underlying holographic thermalization, in dual field theory, also in the far-from-equilibrium regime. (AU)