CFT Hydrodynamics: Symmetries, Exact Solutions and Gravity

TL;DR

This paper explores the symmetries, exact solutions, and gravitational duals of relativistic conformal hydrodynamics, revealing connections to Navier-Stokes equations and domain-wall gravity solutions.

Contribution

It constructs exact relativistic conformal hydrodynamic solutions, analyzes their symmetries, and links these to gravitational dual descriptions, including shock and domain-wall solutions.

Findings

Exact solutions with finite time singularities are constructed.

Relativistic solutions are generated via conformal transformations.

Shock solutions correspond to domain-wall solutions in gravity.

Abstract

We consider the hydrodynamics of relativistic conformal field theories at finite temperature and its slow motions limit, where it reduces to the incompressible Navier-Stokes equations. The symmetries of the equations and their solutions are analyzed. We construct exact solutions with finite time singularities of one-dimensional relativistic conformal hydrodynamic motions, and use them to generate multi-dimensional solutions via special conformal transformations. These solutions, however, are shown to have no non-trivial slow motions limit. A simple non-equilibrium steady state in the form of a shock solution is constructed, and its inner structure is analyzed. We demonstrate that the derivation of the gravitational dual description of conformal hydrodynamics is analogous to the derivation of hydrodynamics equations from the Boltzmann equation. The shock solution is shown to correspond to a domain-wall solution in gravity. We show that the solutions to the non-relativistic incompressible Navier-Stokes equations play a special role in the construction of global solutions to gravity.