Chiral anomaly from (anomalous) spin hydrodynamics

We show that the low energy fluctuations of spinning black Dp branes are described by a theory of spin hydrodynamics on a spacetime ${\mathbb{M}}_{p+1}\times {\mathbb{T}}^{n+2}$ in which the fluid is flowing on ${\mathbb{M}}_{p+1}$ and spinning on ${\mathbb{T}}^{n+2}$. Focusing on the hydrodynamic regime of $\mathcal{N}=4$ supersymmetric Yang-Mills theory, we provide a geometric interpretation of the R-current anomaly in terms of a gravitational anomaly from the ten-dimensional point of view. This follows from the holographic duality between a spinning fluid in ten dimensions and an anomalous chiral fluid in four dimensions. We comment on the relations between the theory of spin hydrodynamics introduced here and other theories of spin hydrodynamics in the context of heavy-ion collisions.