Two-dimensional fluids and their holographic duals

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.

arXiv commentv1: 1+39 pages, Latex, v2: NPB version

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• Bridging Carrollian and Celestial Holography
• The $\Lambda$-BMS${}_4$ Charge Algebra
• Gravitational Edge Modes, Coadjoint Orbits, and Hydrodynamics
• Conformal Carroll Scalars with Boosts
• Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $\sqrt{T\bar{T}}$ deformations
• Charge Algebra in Al(A)dS${}_n$ Spacetimes
• Carrollian hydrodynamics from symmetries
• Carrollian manifolds and null infinity: A view from Cartan geometry
• Universal Corner Symmetry and the Orbit Method for Gravity
• AdS Carroll Chern-Simons supergravity in 2+1 dimensions and its flat limit
• Weyl Charges in Asymptotically Locally AdS${}_3$ Spacetimes
• Holographic Lorentz and Carroll Frames
• Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
• Gauges in Three-Dimensional Gravity and Holographic Fluids
• Flat from anti-de Sitter
• Carrollian fluids and spontaneous breaking of boost symmetry
• Massless Scalars and Higher-Spin BMS in Any Dimension
• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
• Hydro & Thermo Dynamics at Causal Boundaries, Examples in 3d Gravity
• N-extended Chern-Simons Carrollian supergravities in 2+1 spacetime dimensions
• Gravitation in flat spacetime from entanglement
• Ehlers, Carroll, Charges and Dual Charges
• Symmetries and Charges in Weyl-Fefferman-Graham Gauge
• On the Various Extensions of the BMS Group
• Integrable systems and the boundary dynamics of higher spin gravity on AdS${}_3$
• Carrollian limit of quadratic gravity
• Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity
• Radiation in Fluid/Gravity and the Flat Limit
• Asymptotic Limit of Null Hypersurfaces
• Quantization of Carrollian fermions
• Phase space holography with no strings attached
• Two theorems for the gradient expansion of relativistic hydrodynamics
• Supersymmetric Carroll Galileons in Three Dimensions
• One-dimensional Carrollian fluids I: Carroll-Galilei duality
• Field-dependent diffeomorphisms and the transformation of surface charges between gauges
• Carroll black holes in (A)dS and their higher-derivative modifications
• Fefferman-Graham and Bondi Gauges in the Fluid/Gravity Correspondence
• Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars
• Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant
• Free-field construction of Carrollian $W_N$-algebras
• Hirota-Satsuma Dynamics as a Non-Relativistic Limit of KdV Equations
• On the geometric approach to the boundary problem in supergravity