Hydrodynamics of Two-Dimensional CFTs

We demonstrate that the geometric action on a coadjoint orbit of the Virasoro group appropriately describes non-dissipative two-dimensional conformal fluids. While this action has already appeared in the context of AdS3 gravity, the hydrodynamical interpretation given here is new. We use this to argue that the geometric action manifestly controls both sides of the fluid/gravity correspondence, and that the gravitational ‘hologram’ gives an effective hydrodynamical description of the dual CFT. As a byproduct, our work sheds light on the nature of the AdS3 reparametrization theory used to effectively compute Virasoro vacuum blocks at large central charge, since the reparametrization mode is now understood as a fluctuation of the fluid velocity.