Based on a holographic model incorporating both chiral anomaly and gravitational anomaly, we study the effect of magneto-vortical coupling on transport properties of a strongly coupled plasma. The focus of present work is on the generation of a vector charge density and an axial current, as response to vorticity in a magnetized plasma. The transport coefficients parameterising the vector charge density and axial current are calculated both analytically (in the weak magnetic field limit) and also numerically (for general values of the magnetic field). We find the generation of vector charge receives both non-anomalous and anomalous contributions, with the non-anomalous contribution dominating in the limit of strong magnetic field and the anomalous contribution sensitive to both chiral anomaly and gravitational anomaly. On the contrary, we find the axial current is induced entirely due to the gravitational anomaly, thus we interpret the axial current generation as chiral vortical effect. The corresponding chiral vortical conductivity is found to be suppressed by the magnetic field. By Onsager relation, these transport coefficients are responsible for the generation of a thermal current due to a transverse electric field or a transverse axial magnetic field, which we call thermal Hall effect and thermal axial magnetic effect, respectively.
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