Two-dimensional fluids and their holographic duals

TL;DR

The paper develops a unified framework to reconstruct three-dimensional spacetimes with locally AdS or locally Minkowski geometry from two-dimensional fluid data, using EF coordinates and allowing general curved boundaries. It shows that conformal anomalies and dissipative data (heat current) crucially shape the bulk reconstruction and the resulting symmetry algebras (Virasoro for AdS and BMS3 for flat space). By analyzing both relativistic and Carrollian 2D fluids, the authors reveal that hydrodynamic-frame choices can alter global bulk properties, and that a residual frame invariance persists in the Carrollian (flat) limit. The work thus clarifies how dissipation and frame freedom interface with holography in three dimensions, and it lays groundwork for exploring more general asymptotics and higher-dimensional extensions.

Abstract

We describe the dynamics of two-dimensional relativistic and Carrollian fluids. These are mapped holographically to three-dimensional locally anti-de Sitter and locally Minkowski spacetimes, respectively. To this end, we use Eddington-Finkelstein coordinates, and grant general curved two-dimensional geometries as hosts for hydrodynamics. This requires to handle the conformal anomaly, and the expressions obtained for the reconstructed bulk metrics incorporate non-conformal-fluid data. We also analyze the freedom of choosing arbitrarily the hydrodynamic frame for the description of relativistic fluids, and propose an invariant entropy current compatible with classical and extended irreversible thermodynamics. This local freedom breaks down in the dual gravitational picture, and fluid/gravity correspondence turns out to be sensitive to dissipation processes: the fluid heat current is a necessary ingredient for reconstructing all Banados asymptotically anti-de Sitter solutions. The same feature emerges for Carrollian fluids, which enjoy a residual frame invariance, and their Barnich-Troessaert locally Minkowski duals. These statements are proven by computing the algebra of surface conserved charges in the fluid-reconstructed bulk three-dimensional spacetimes.