An effective action for diffusion of a conserved U(1) charge is derived to all orders in the derivative expansion within a holographic model dual to the Schwinger-Keldysh closed time path. A systematic approach to solution of the 5D Maxwell equations in a doubled Schwarzschild-AdS5 black brane geometry is developed. Constitutive relation for the stochastic charge current is shown to have a term induced by thermal fluctuations (coloured noise). All transport coefficient functions parameterising the effective action and constitutive relations are computed analytically in the hydrodynamic expansion, and then numerically for finite momenta.

Nonlinear transport phenomena induced by chiral anomaly are explored within a 4D field theory defined holographically as U (1) V ×U (1) A Maxwell-Chern-Simons theory in Schwarzschild-AdS 5 . In presence of weak constant background electromagnetic fields, the constitutive relations for vector and axial currents, resummed to all orders in the gradients of charge densities, are encoded in nine momenta-dependent transport coefficient functions (TCFs). These TCFs are first calculated analytically up to third order in gradient expansion, and then evaluated numerically beyond the hydrodynamic limit. Fourier transformed, the TCFs become memory functions. The memory function of the chiral magnetic effect (CME) is found to differ dramatically from the instantaneous response form of the original CME. Beyond hydrodynamic limit and when external magnetic field is larger than some critical value, the chiral magnetic wave (CMW) is discovered to possess a discrete spectrum of non-dissipative modes.

Nonlinear transport phenomena induced by the chiral anomaly are explored within a 4D field theory defined holographically as U (1) V × U (1) A Maxwell-Chern-Simons theory in Schwarzschild-AdS 5 . First, in presence of external electromagnetic fields, a general form of vector and axial currents is derived. Then, within the gradient expansion up to third order, we analytically compute all (over 50) transport coefficients. A wealth of higher order (nonlinear) transport phenomena induced by chiral anomaly are found beyond the Chiral Magnetic and Chiral Separation Effects. Some of the higher order terms are relaxation time corrections to the lowest order nonlinear effects. The charge diffusion constant and dispersion relation of the Chiral Magnetic Wave are found to receive anomaly-induced nonlinear corrections due to e/m background fields. Furthermore, there emerges a new gapless mode, which we refer to as Chiral Hall Density Wave, propagating along the background Poynting vector.

We study rapidly spinning compact stars with equations of state featuring a first-order phase transition between strongly coupled nuclear matter and deconfined quark matter by employing the gauge/gravity duality. We consider a family of models that allow purely hadronic uniformly rotating stars with masses up to approximately 2.9 M ⊙, and are therefore compatible with the interpretation that the secondary component ( ) in GW190814 is a neutron star. These stars have central densities that are several times the nuclear saturation density, so that strong coupling and non-perturbative effects become crucial. We construct models where the maximal mass of static (rotating) stars M TOV (M max) is either determined by the secular instability or a phase-transition induced collapse. We find the largest values for M max/M TOV in cases where the phase transition determines M max, which shifts our fit result to , a value slightly above the Breu–Rezzolla bound inferred from models without phase transition.