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We show that the recently measured UV luminosity functions of ultra-faintlensed galaxies at z= 6 in the Hubble Frontier Fields provide an unprecedentedprobe for the mass m_X of the Warm Dark Matter candidates independent ofbaryonic physics. Comparing the measured abundance of the faintest galaxieswith the maximum number density of dark matter halos in WDM cosmologies sets arobust limit m_X> 2.9 keV for the mass of thermal relic WDM particles at a1-sigma confidence level, m_X> 2.4 keV at 2-sigma, and m_X> 2.1 keV at 3-sigma.These constitute the tightest constraints on WDM particle mass derived to dateindependently of the baryonic physics involved in galaxy formation. We discussthe impact of our results on the production mechanism of sterile neutrinos. Inparticular, if sterile neutrinos are responsible for the 3.5 keV line reportedin observations of X-ray clusters, our results firmly rule out theDodelson-Widrow production mechanism, and yield m_{sterile}> 6.1 keV forsterile neutrinos produced via the Shi-Fuller mechanism.

A Stringent Limit on the Warm Dark Matter Particle Masses from the Abundance of z=6 Galaxies in the Hubble Frontier Fields