Near-Light-Cone Nonhydrodynamic Structure from Boosted Hydrodynamics

Hydrodynamics provides a universal description of many-body systems at long wavelengths. Its long-lived collective excitations, known as hydrodynamic modes, admit long-wavelength expansions whose convergence is encoded in the analytic structure of retarded correlators of conserved quantities in thermal equilibrium. We show that a boost can change which nonhydrodynamic singularity limits such an expansion. At large boost, the relevant singularity originates in the large-momentum, near-light-cone region of the rest-frame spectrum. After removing the Lorentz-factor growth, the rescaled convergence scale is controlled by the microscopic spectral structure of the theory. We explicitly demonstrate this in two examples: relaxation-time kinetic theory and holography.