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.
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 2 Michal P. Heller,
- 2 Alexandre Serantes,
- 2 3 Michal Spalinski,
- 1 2 Viktor Svensson,
- 4 Benjamin Withers
- 1 Max-Planck-Institut für Gravitationsphysik / Max Planck Institute for Gravitational Physics [AEI]
- 2 Narodowe Centrum Badań Jądrowych / National Centre for Nuclear Research [NCBJ]
- 3 Uniwersytet w Białymstoku / University of Białystok [UwB]
- 4 University of Southampton