Convergence of hydrodynamic modes: insights from kinetic theory and holography

• Main Author: Michal P. Heller, Alexandre Serantes, Michał Spaliński, Viktor Svensson, Benjamin Withers
• Format: Article
• Language: English
• Published: SciPost 2021-06-01
• Series: SciPost Physics
• Online Access: https://scipost.org/SciPostPhys.10.6.123

We study the mechanisms setting the radius of convergence of hydrodynamic dispersion relations in kinetic theory in the relaxation time approximation. This introduces a qualitatively new feature with respect to holography: a nonhydrodynamic sector represented by a branch cut in the retarded Green's function. In contrast with existing holographic examples, we find that the radius of convergence in the shear channel is set by a collision of the hydrodynamic pole with a branch point. In the sound channel it is set by a pole-pole collision on a non-principal sheet of the Green's function. More generally, we examine the consequences of the implicit function theorem in hydrodynamics and give a prescription to determine a set of points that necessarily includes all complex singularities of the dispersion relation. This may be used as a practical tool to assist in determining the radius of convergence of hydrodynamic dispersion relations.