Shear viscosity from thermal fluctuations in relativistic conformal fluid dynamics

J. PERALTA RAMOS; ESTEBAN CALZETTA

JOURNAL OF HIGH ENERGY PHYSICS - (Online)

SISSA

Lugar: Trieste; Año: 2012 vol. 2 p. 1 - 25

1029-8479

Within the framework of relativistic fluctuating hydrodynamics we computethe contribution of thermal fluctuations to the effective infrared shear viscosity of a conformalfluid, focusing on quadratic (in fluctuations), second order (in velocity gradients)terms in the conservation equations. Our approach is based on the separation of hydrodynamicfields in soft and ultrasoft sectors, in which the effective shear viscosity arises dueto the action of the soft modes on the evolution of the ultrasoft ones. We find that for astrongly coupled fluid with small shear viscosity-to-entropy ratio η/s the contribution ofthermal fluctuations to the effective shear viscosity is small but significant. Using realisticestimates for the strongly coupled quark-gluon plasma created in heavy ion collisions, wefind that for η/s close to the AdS/CFT lower bound 1/(4π) the correction is positive andat most amounts to 10% in the temperature range 200?300MeV, whereas for larger valuesη/s ∼ 2/(4π) the correction is negligible. For weakly coupled theories the correction isvery small even for η/s = 0.08 and can be neglected.