Fluid/gravity correspondence

It is well known that non-relativistic incompressible viscous fluids are described by the Navier-Stokes equations. Fluid dynamical evolution of a system shows many challenging properties like turbulence whose detailed understanding is still missing. The hydrodynamic behavior of the system is characterized by a set of transport coefficients, like shear viscosity, bulk viscosity etc. A holographic description of the fluid dynamical system provides a new perspective on the problem. One can apply this toolkit to compute different transport coefficients of strongly coupled plasma. Although, the fluid/gravity correspondence predicts properties of a relativistic conformal fluid, the generalization of the correspondence to non-relativistic (also non-conformal) systems exists and we will discuss about those issues subsequently.
After Relativistic Heavy Ion Collider (RHIC) experiments, the study of shear viscosity to entropy density ratio of gauge theory plasma has developed lots of attention. The QGP (Quark-Gluon Plasma) produced at RHIC behaves like viscous fluid with very small shear viscosity coefficient (near-perfect fluid). Such a low ratio of shear viscosity to entropy density is very hard to describe with conventional method. Usual perturbative gauge theory computations or lattice gauge theory technique are not applicable to explain RHIC results. Holographic techniques (motivated from the AdS/CFT correspondence) to compute hydrodynamic transport coefficients exhibit a remarkable quantitative agreement with those arising from numerical fits to RHIC data.