# Conformal field theory as microscopic dynamics of incompressible Euler and Navier-Stokes equations.

@article{Fouxon2008ConformalFT, title={Conformal field theory as microscopic dynamics of incompressible Euler and Navier-Stokes equations.}, author={Itzhak Fouxon and Yaron Oz}, journal={Physical review letters}, year={2008}, volume={101 26}, pages={ 261602 } }

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental…

## 61 Citations

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## References

SHOWING 1-10 OF 21 REFERENCES

Relativistic viscous hydrodynamics, conformal invariance, and holography

- Physics, Mathematics
- 2008

We consider second-order viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the second-order…

From quantum field theory to hydrodynamics: Transport coefficients and effective kinetic theory.

- PhysicsPhysical review. D, Particles and fields
- 1996

The evaluation of hydrodynamic transport coefficients in relativistic field theory, and the emergence of an effective kinetic theory description, is examined. Even in a weakly coupled scalar field…

Nonlinear fluid dynamics from gravity

- Physics
- 2008

Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields—arbitrary functions of…

Local Fluid Dynamical Entropy from Gravity

- Physics, Mathematics
- 2008

Spacetime geometries dual to arbitrary fluid flows in strongly coupled N=4 super Yang Mills theory have recently been constructed perturbatively in the long wavelength limit. We demonstrate that…

Particles and fields in fluid turbulence

- Physics
- 2001

The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to…

Conformal invariance in two-dimensional turbulence

- Physics, Mathematics
- 2006

The simplicity of fundamental physical laws manifests itself in fundamental symmetries. Although systems with an infinite number of strongly interacting degrees of freedom (in particle physics and…

Inverse turbulent cascades and conformally invariant curves.

- PhysicsPhysical review letters
- 2007

It is shown that temperature isolines are statistically equivalent to curves that can be mapped into a one-dimensional Brownian walk (called Schramm-Loewner evolution or SLEkappa) and that conformal invariance may be expected for inverse turbulent cascades of strongly interacting systems.

Bound on viscosity and the generalized second law of thermodynamics

- Physics
- 2008

We describe a new paradox for ideal fluids. It arises in the accretion of an ideal fluid onto a black hole, where, under suitable boundary conditions, the flow can violate the generalized second law…

An Introduction to Fluid Dynamics

- Economics, Education
- 1968

Keywords: dynamique des : fluides Reference Record created on 2005-11-18, modified on 2016-08-08