Hydrodynamics of two-dimensional CFTs

TL;DR

This paper shows that a geometric action on the Virasoro group's coadjoint orbit effectively describes non-dissipative 2D conformal fluids and links this to the fluid/gravity correspondence, providing new insights into AdS$_3$ holography.

Contribution

It introduces a hydrodynamical interpretation of the geometric action on Virasoro coadjoint orbits, connecting it to 2D CFT hydrodynamics and holography.

Findings

The geometric action describes non-dissipative 2D conformal fluids.

It clarifies the role of reparametrization modes as fluid velocity fluctuations.

The work links the fluid description to AdS$_3$ gravity and Virasoro vacuum blocks.

Abstract

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 had already appeared in the context of AdS$_3$ 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, where the gravitational `hologram' gives an effective hydrodynamical description of the dual CFT. As a byproduct, our work sheds light on the nature of the AdS$_3$ reparametrization theory used to effectively compute Virasoro vacuum blocks at large central charge, as the reparametrization mode is now understood as a fluctuation of the fluid velocity.