Anomalous Transport and Hydro-Gravity Duality

By anomalous transport one understands transport driven by the chiral anomalies of quantum field theory (QFT). In our case it is mostly axial current in hydrodynamical set up. The notion of duality assumes existence of two different theories whose predictions for a certain class of observables coincide with each other. In our case the observables are matrix elements of external probes, such as energy-momentum tensor or axial current, as functions of acceleration and angular velocity of the medium. Two approaches to evaluate these observables are provided by thermodynamics and by theory of motion in external gravitational fields. The corresponding duality was introduced by the authors in the year 2019. We reiterate the basic points of the argumentation and highlight new points brought in by later development.