Determination of the Shear Viscosity Relaxation Time at Weak and Strong Coupling

TL;DR

This paper clarifies how to accurately determine the shear viscosity relaxation time in relativistic fluids, highlighting the limitations of gradient expansion and emphasizing the role of non-hydrodynamic poles, especially in strongly coupled theories.

Contribution

It demonstrates that the shear viscosity relaxation time should be derived from the retarded Green's function's poles, challenging the conventional gradient expansion approach and revealing differences in strongly coupled theories.

Findings

Gradient expansion can be ambiguous for relaxation time extraction.

Shear viscosity relaxation time is linked to the slowest non-hydrodynamic pole.

In strongly coupled theories, poles have nonzero real parts, affecting fluid dynamics equations.

Abstract

We investigate the microscopic origin of the relaxation time coefficient in relativistic fluid dynamics. We show that the extraction of the shear viscosity relaxation time via the gradient expansion is ambiguous and in general fails to give the correct result. The correct value for the shear viscosity relaxation time is extracted from the slowest non-hydrodynamic pole of the corresponding retarded Green's function, if such a pole is purely imaginary. According to the AdS/CFT correspondence, in strongly-coupled $\mathcal{N}=4$ SYM the non-hydrodynamic poles of the shear stress tensor nearest to the origin have a nonzero real part, which implies that the transient fluid-dynamical equations for this gauge theory are not equivalent to the well-known Israel-Stewart equations.