Convergence of hydrodynamic modes: insights from kinetic theory and holography

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