# Two-dimensional fluids and their holographic duals

## TL;DR

This paper explores the holographic duality between two-dimensional relativistic and Carrollian fluids and their three-dimensional gravitational counterparts, analyzing the effects of conformal anomalies, frame choices, and dissipation on the fluid/gravity correspondence.

## Contribution

It provides a detailed holographic mapping of 2D fluids to 3D spacetimes, including the handling of anomalies and the impact of dissipation on the dual gravitational solutions.

## Key findings

- Holographic duals are constructed for 2D fluids in curved geometries.
- Fluid heat current is essential for reconstructing AdS solutions.
- Frame invariance is broken in the gravitational duals, revealing dissipation effects.

## 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.